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1
Content available remote Topology from Neighbourhoods
100%
Coghetto R.
Formalized Mathematics
|
2015
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tom 23
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nr 4
289-296
EN
Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x in this topology. We present a correspondence between a topological space and a space defined with the formal topological space structure with the three U-FMT conditions called the topology from neighbourhoods. For the formalization, we were inspired by the works of Bourbaki [11] and Claude Wagschal [31].
2
Content available remote Topologický prostor jako model bytí v pozdních pracovních poznámkách Maurice Merleau-Pontyho
100%
Nitsche M.
Filosofický časopis (Philosophical Journal)
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2010
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tom 58
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nr 1
49-56
EN
This interpretational sketch focuses on a reading of several remarks about “topological space” as a “model of being” in Merleau-Ponty’s notes towards a projected work, the torso of which was published under the title The Visible and the Invisible. The reason for choosing topological space as a model of being is, on the present interpretation, because it constitutes an attempt to find a place for consciousness which does not bring with it the requirement of underpinning the world.
3
Content available remote Some fixed point theorems for mappings satisfying contractive condition of integral type on d-complete topological spaces
100%
Altun I. , Turkoglu D.
Fasciculi Mathematici
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2009
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tom 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.
4
Content available remote On totally πg-continuous functions
100%
Noiri T. , Bhuvaneswari J. , Rajesh N.
Fasciculi Mathematici
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2013
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tom Nr 50
101--108
EN
In this paper, πg-closed sets and πg-open sets are used to define and investigate a new class of functions called, totally πg-continuous functions. Relationships between this new class and other classes of related functions are established.
5
Content available remote On upper and lower faintly δ-β-continuous multifunctions
100%
Jafari S. , Noiri T. , Popa V. , Rajesh N.
Fasciculi Mathematici
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2011
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tom Nr 46
77--85
EN
In this paper, we introduce and study a new class of multifunctions called faintly δ-β-continuous multifunctions in topological spaces
6
Content available remote New maximal and minimal sets via βθ-open sets
88%
Caldas M. , Jafari S. , Noiri T.
Fasciculi Mathematici
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2018
|
tom Nr 61
17--25
EN
Nakaoka and Oda ([9] and [10]) introduced the notion of maximal open sets and minimal closed sets. In this paper, we introduce new classes of sets called maximal βθ-open sets, minimal βθ-closed sets, βθ-semi maximal open sets and βθ-semi minimal closed sets and investigate some of their fundamental properties.
7
Content available remote Modification of Near Sets Theory
88%
Marei E. A. , Abd El-Monsef M. E. , Abu-Donia H. M.
Fundamenta Informaticae
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2015
|
tom Vol. 137, nr 3
387--402
EN
Most real life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subsets without coding or using assumption. The aim of this paper is to introduce different approaches to near sets by using general relations and special neighborhoods. Some fundamental properties and characterizations are given. We obtain a comparison between these new approximations and traditional approximations introduced by Peters [23].
8
Content available Topological Properties and Methodology of Research of Complex Logistic Systems Efficiency
88%
Zhivitskaya H.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2014
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tom Vol. 3, No 3
23--32
EN
It is indicated that sets of elements of complex logistic system, their parameters, numerical values, properties and finally – structures of complex logistic system, are topological spaces between which properties of homeomorphism can exist, that allows to apply mathematical apparatus of the theory of topology at the solution of a number of tasks. The general principles of an estimation of efficiency of functioning of logistical complexes on the basis of modeling with the account of hierarchical construction and influence of the human factor are considered.
9
Content available remote Unifying Rough Set Theories via Large Scaled Granular Computing
88%
Lin T. Y. , Liu Y. , Huang W.
Fundamenta Informaticae
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2013
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tom Vol. 127, nr 1-4
413--428
EN
This paper explains the mathematics of large scaled granular computing (GrC), augmented with a new Knowledge theory, by unifying rough set theories (RS) into one single concept, namely, neighborhood systems (NS). NS was first introduced in 1989 by T. Y. Lin to capture the concepts of “near” (topology) and “conflict” (security). Since 1996 when the term Granular Computing (GrC) was coined by T. Y. Lin to label Zadeh's vision, NS has been pushed into the “heart” of GrC. In 2011, LNS, the largest NS, was axiomatized; it implied that this set of axioms defines a new mathematics that realizes Zadeh's vision. The main messages are: this new mathematics is powerful and practical.
10
Content available About the ways of defining connected sets in the topological spaces
75%
Domańska K. , Wróbel M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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tom 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.
11
Content available On cluster sets of connected functions
75%
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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tom 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.
12
Content available remote Remarks on connectivity and I-connectivity
75%
Jędrzejewski J. , Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
49-54
13
Content available remote Remarks on almost locally connected spaces
75%
Shahzad N. , Al-Malki N.
Demonstratio Mathematica
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2006
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tom Vol. 39, nr 1
219-222
EN
Some preservation theorems for almost local connectedness are proved.
14
Content available remote Problem of the existence of ω*-primitives
75%
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
|
tom Vol. 12
61-68
EN
lf (X, ᵨ) is a dense in itself metric space and f : X →ℝ, then we define ω*(f,x) = infr >0 supy,z∈B (x,r) \ {x} ׀ f(y) - f(z)׀. We say that a function F : X →ℝ is an ω*-primitive for f : X →ℝ if ω* (F, .) = f. We discuss problem of the existence of ω*-primitives for an arbitrary upper semicontinuous function f : X → [0, ∞ ) defined on a dense in itself metric space. At the end we show that if an upper semicontinuous function f : X → [0, ∞) is defined on a nonmetrizable topological space, then ω*-primitive may not exists.
15
Content available remote Pβ-connectedness in topological spaces
75%
Tyagi B. K. , Singh S. , Bhardwaj M.
Demonstratio Mathematica
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2017
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tom 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.
16
Content available remote Rough Granular Computing in Modal Settings : Generalised Approximation Spaces
75%
Wolski M. , Gomolińska A.
Fundamenta Informaticae
|
2016
|
tom Vol. 148, nr 1/2
157--172
EN
The paper studies the rough granular computing paradigm within the conceptual settings of multi-modal logic. The main idea is to express a generalised approximation space (U; I; κ), where U is the universe of objects, I is an uncertainty function, and κ is a rough inclusion function, in terms of binary relations, and then to consider the corresponding modal operators. The new modal structure obtained in this way is rich enough to define closure and interior operators corresponding to the classical rough approximation operators and their well-known uni-modal generalisations. In contrast to the standard modal interpretation of rough set approximations, in the new settings one can directly deal with information granules and their properties, which is crucial for granular computing paradigm. More precisely, we are provided with means of describing features of objects and information granules, as well as inclusion degrees between granules.
17
Content available remote On almost normality
75%
Kalantan L. , Allahabi F.
Demonstratio Mathematica
|
2008
|
tom Vol. 41, nr 4
961-968
EN
A topological space X is called almost normal if for any two disjoint closed subsets A and B of X one of which is regularly closed, there exist two open disjoint subsets U and V of X such that A C U and B C V. We will present an example of a Tychonoff almost normal space which is not normal. Almost normality is not productive. We will present some conditions to assure that the product of two spaces will be almost normal.
18
Content available remote On (γ, γ')-preopen sets
75%
Carpintero C. , Rajesh N. , Rosas E.
Demonstratio Mathematica
|
2013
|
tom Vol. 46, nr 3
617--629
EN
In this paper, we introduce and study the concept of [γ, γ']-preopen sets in topological space.
19
On a typological model of von Bertalanffy's systems
63%
Korczyński W.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Elektryka
|
2005
|
tom Z. 42
219-226
EN
In the paper a generalization of the classical (see [1]) notion of hypergraphs is described and a topological presentation of them is presented. It is shown that a counterpart of the well known notion of directed graph may be used as a model of von Bertalanffy's systems.
PL
W pracy opisano pewne uogólnienie klasycznego pojęcia hipergrafu (por. [1]). Pokazano również, że pewien analogon dobrze znanego pojęcia grafu skierowanego może być używany jako model systemów von Bertalanffy-ego.
20
Content available On the quasi-uniform convergence
63%
Drozdowski R. , Jędrzejewski J. , Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
tom 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].
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