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1
Content available remote On almost e-I-continuous functions
AL-Omeri Wadei, Noiri Takashi
Demonstratio Mathematica
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2021
|
Vol. 54, nr 1
168--177
EN
This work is concerned with a new class of functions called almost e-I-continuous functions containing the class of almost e-continuous functions. This notion is stronger than almost δβI-continuous functions and is weaker than both almost e-continuous functions and e-I-continuous functions. Relationships between this new class and other classes of functions are investigated and some characterizations of this new class of functions are studied.
2
Content available remote Two new forms of ordered soft separation axioms
Al-shami Tareq M., El-Shafei Mohammed E.
Demonstratio Mathematica
|
2020
|
Vol. 53, nr 1
8--26
EN
The goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft Ti-ordered and strong soft Ti-ordered spaces (i = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary points and the distinction between them is attributed to the nature of the monotone neighborhoods. We provide several examples to elucidate the relationships among these concepts and to show the relationships associate them with their parametric topological ordered spaces and p-soft Ti-ordered spaces. Some open problems on the relationships between strong soft Ti-ordered and soft Ti-ordered spaces (i = 2, 3, 4) are posed. Also, we prove some significant results which associate both types of the introduced ordered axioms with some notions such as finite product soft spaces, soft topological and soft hereditary properties. Furthermore, we describe the shape of increasing (decreasing) soft closed and open subsets of soft regularly ordered spaces; and demonstrate that a condition of strong soft regularly ordered is sufficient for the equivalence between p-soft T1-ordered and strong soft T1-ordered spaces. Finally, we establish a number of findings that associate soft compactness with some ordered soft separation axioms initiated in this work.
3
Content available remote Two types of separation axioms on supra softtopological spaces
Al-shami Tareq M., El-Shafei Mohammed E.
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
147--165
EN
In 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft Ti-spaces and supra p-soft Ti-spaces for i= 0,1,2,3,4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions. We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft Ti-spaces are finer than supra soft Ti-spaces in the case of i= 0,1,4; and we demonstrate that supra soft T3-spaces are finer than supra p-soft T3-spaces. We point out that supra p-softTi-axioms imply supra p-softTi−1, however, this characterization does not hold for supra soft Ti-axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft Ti-spaces (i= 1,2) and supra p-soft regular spaces. Moreover, we define the finite product of supra soft spaces and manifest that the finite product of supra soft Ti (supra p-soft Ti) is supra soft Ti (supra p-soft Ti) for i= 0,1,2,3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft S*-continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.
4
Topologia klastrowa w modelu logistyki biznesu
Logistyka
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2018
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nr 6
25--29
PL
Artykuł przedstawia zagadnienia szeroko rozumianego modelu logistyki biznesu w aspekcie opcji jego tworzenia i przeprojektowania. Analizy poprowadzono poprzez identyfikację struktur jednolitych topologicznie i struktur klasterowych w odniesieniu do typowania form modelu biznesu. Prezentowane treści mogą być pomocne w analizach projektowych ładu przestrzennego, jak również projektach infrastrukturalnych, zarządczych. Zainicjowanie spojrzenia matematyczno- wizualizacyjnego i sformułowanej na tej podstawie metodyki badań projektowych może stanowić o nowum spojrzenia badawczego z wykorzystaniem miernika topologicznego.
EN
The article presents the issues of broadly defined business logistic’s model in the aspect of its creating and redesigning options. The analyses have been carried out through identification of topologically uniform structures and claster in respect of spacial planning typing business model. The presented content may be useful in project analyses of spacial order, as well as in infrastructural management project. Initiating a mathematical-visualisational view and a methodology of project research formulated upon this view may determine an innovative research perspective using the topology measure.
5
Content available remote Degree of (L, M)-fuzzy semi-precontinuous and (L, M)-fuzzy semi-preirresolute functions
Al-Omeri W. F., Khalil O. H., Ghareeb A.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
182--197
EN
The aim of this paper is to present the degree of semi-preopenness, semi precontinuity, and semi-preirresoluteness for functions in (L, M)-fuzzy pretopology with the help of implication operation and (L, M)-fuzzy semi-preopen operator introduced by [Ghareeb A., L-fuzzy semi-preopen operator in L-fuzzy topological spaces, Neural Comput. & Appl., 2012, 21, 87–92]. Further, we generalize the properties of semi-preopenness, semi-precontinuity and semi-preirresoluteness to (L, M)-fuzzy pretopological setting relying on graded concepts. Also, we discuss their relationships with the corresponding degrees of semi-precompactness, semi-preconnectedness and semi-preseparation axioms.
6
Content available remote The algebras of bounded and essentially bounded Lebesgue measurable functions
Mortini R., Rupp R.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
94--99
EN
Let X be a set in Rn with positive Lebesgue measure. It is well known that the spectrum of the algebra L∞(X) of (equivalence classes) of essentially bounded, complex-valued, measurable functions on X is an extremely disconnected compact Hausdorspace. We show, by elementary methods, that the spectrum M of the algebra Lb(X, C) of all bounded measurable functions on X is not extremely disconnected, though totally disconnected. Let ∆ = {δx : x ∈ X} be the set of point evaluations and let g be the Gelfand topology on M. Then (∆, g) is homeomorphic to (X, Tdis), where Tdis is the discrete topology. Moreover, ∆ is a dense subset of the spectrum M of Lb(X, C). Finally, the hull h(I), (which is homeomorphic to M(L∞(X))), of the ideal of all functions in Lb(X, C) vanishing almost everywhere on X is a nowhere dense and extremely disconnected subset of the Corona M \ ∆ of Lb(X, C).
7
Content available remote Pβ-connectedness in topological spaces
Tyagi B. K., Singh S., Bhardwaj M.
Demonstratio Mathematica
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2017
|
Vol. 50, nr 1
299--308
EN
A new property called Pβ-connectedness is introduced which is stronger than connectedness and equivalent to pre-connectedness. The properties of this notion are explored and its relationship with other forms of connectedness, for example hyperconnectedness etc. are discussed. Locally pre-indiscrete spaces are defined as the spaces in which pre-open sets are closed. In such spaces connectedness becomes equivalent to pre-connectedness and hence to Pβ-connectedness, and semi-connectedness becomes equivalent to Pβ-connectedness. The notion of locally Pβ-connected space is introduced. The behavior of Pβ-connectedness under several types of mappings is investigated. An intermediate value theorem is obtained.
8
Content available About the ways of defining connected sets in the topological spaces
Domańska K., Wróbel M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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Vol. 21
11--16
EN
A topological space is called connected if it is not the union of two disjoint, nonempty and open sets in this space. The standard exercises show that here the concept of open sets can be replaced by closed sets or separated sets. In this context we will discuss the definition of connected sets in topological spaces, not being the whole space with particular regard to metric spaces, without the term of subspace topology.
9
Content available On e-I-open sets, e-I-continuous functions and decomposition of continuity
Al-Omeri W., Noorani M.S.M., Al-Omari A.
Journal of Mathematics and Applications
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2015
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Vol. 38
15--31
EN
In this paper, we introduce the notations of e-I-open sets and strong B*I -set to obtain a decomposition of continuing via idealization. Additionally, we investigate properties of e-I-open sets and strong B*I -set. Also we studied some more properties of e-I-open sets and obtained several characterizations of e-I-continuous functions and investigate their relationship with other types of functions.
10
Content available remote Brutalist games involving physical movement
Niebrzydowski W.
Czasopismo Techniczne. Architektura
|
2015
|
Y. 112, iss. 9-A
233--237
EN
Brutalist architecture is widely regarded as gloomy and unfriendly. At its origin was the post-war austerity, but also a fascination with the child and its way of seeing the world. Therefore it is not surprising that the space and forms of brutalist buildings should be perceived by people moving along the routes designed by architects and discovering new views in a dynamic way. This peculiar spatial game is full of surprises and even jokes.
PL
Architektura brutalistyczna powszechnie uważana jest za ponurą i nieprzyjazną. U jej genezy rzeczywiście stoi powojenna surowość, ale także fascynacja dzieckiem i jego sposobem widzenia świata. Nie powinno zatem zaskakiwać, że przestrzeń i formy brutalistycznych obiektów należy poznawać w ruchu, przemieszczając się wzdłuż dróg wyznaczonych przez projektantów i odkrywając nowe widoki. W tej swoistej zabawie przestrzenią nie brakuje zaskoczeń a nawet żartów.
11
Content available remote Rδ-supercontinuous functions
Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
433--448
EN
A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).
12
Content available remote Supra b-compact and supra b-Lindelöf spaces
Mustafa J. M.
Journal of Mathematics and Applications
|
2013
|
Vol. 36
79--83
EN
In this paper we introduce the notion of supra b-compact spaces and investigate its several properties and characterizat eions. Also we introduce and study the notion of supra b-Lindelöf spaces.
13
Content available remote On (γ, γ')-preopen sets
Carpintero C., Rajesh N., Rosas E.
Demonstratio Mathematica
|
2013
|
Vol. 46, nr 3
617--629
EN
In this paper, we introduce and study the concept of [γ, γ']-preopen sets in topological space.
14
Content available On local Whitney convergence
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2012
|
Vol. 17
57-68
EN
In this paper we will give definitions of local Whitney convergence in F(X,Y ) and in C(X,Y ), where X is a topological space, (Y,d) is a metric space and F(X,Y ) is the space of all functions from X to Y and C(X,Y ) is the space of all continuous functions from X to Y . We will study some properties of this notion and connections with other kinds of convergence.
15
Content available On the quasi-uniform convergence
Drozdowski R., Jędrzejewski J., Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
Vol. 16
19--22
EN
Arzelá [1] considered the weaker form of uniform convergence which is as good as uniform convergence of sequences of functions in respect to continuity of the limit of a sequence of continuous functions. Some generalization of such convergence can be found in [5]. Similar kinds of convergence of function sequences were considered in [3] and [4]. In our article we generalize those kinds of convergence for functions defined in a topological space with values in a topological space. In the article we use terminology which is explained in Engelking's monograph “General Topology” [2]. Among others, we use the notion of a star with respect to an open over. If X is a topological space and α is a cover of this space, then the star St(x, α) of a point x ϵ X with respect to the cover α is defined as the union of all the sets from α which contain the point x, i.e. [wzór].
16
Content available remote On weakly BR-open functions and their characterizations in topological spaces
Caldas M., Ekici E., Jafari S., Latif R. M.
Demonstratio Mathematica
|
2011
|
Vol. 44, nr 1
159--168
EN
In this paper, we introduce and study a new class of functions by using the notions of b-θ-open sets and b-θ-closure operator called weakly BR-open functions. The connections between this function and the other existing topological functions are studied.
17
Content available remote Operations on bitopological spaces
Khedr F. H., Abdelhakiem K. M.
Fasciculi Mathematici
|
2010
|
Nr 45
47--57
EN
In 1979, Kasahara [8], introduced the concept of operations on topological spaces. Further investigations of this concept are given in [7,15]. Operations on bitopological spaces were discussed in some manner in [ 1,10]. In this paper we use a different technique of that in [1,10] to study the concepts of operations on bitopological spaces by generalizing the results obtained in [8,15] to such spaces.
18
Content available On cluster sets of connected functions
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
51-61
EN
In the article we discuss some properties of a few classes of connected functions and cluster sets of functions from those classes.
19
Content available remote Some fixed point theorems for mappings satisfying contractive condition of integral type on d-complete topological spaces
Altun I., Turkoglu D.
Fasciculi Mathematici
|
2009
|
Nr 42
5-15
EN
In this paper, we prove two fixed point theorems for mappings satisfying contractive condition of integral type on d-complete Hausdorff topological spaces.
20
Content available remote Remarks on connectivity and I-connectivity
Jędrzejewski J., Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
49-54
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