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1
Content available remote On contra (…)-continuous functions and strongly (…)-closed spaces
100%
Missier S. P. , Devamanoharan C. , Caldas M. , Jafari S.
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2012
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tom Vol. 45, nr 1
187-202
EN
In [4], Dontchev introduced and investigated a new notion of continuity called contra-continuity. Recently, Jafari and Noiri ([8], [9], [10]) introduced new generalization of contra-continuity called contra-super-continuity, contra-(…)-continuity and contra-precontinuity. It is the objective of this paper to introduce and study a new class of contra-continuous functions via (…)-closed sets.
2
Content available remote Topological Interpretation of Rough Sets
80%
Grabowski A.
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nr 1
89-97
EN
Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and about fourteen sets of Kuratowski [17] (encoded with the help of Mizar adjectives and clusters’ registrations in [1]) in terms of rough approximations. The upper bounds which were 14 and 7 in the original paper of Kuratowski, in our case are six and three, respectively. It turns out that within the classification given by Isomichi, 1st class subsets are precisely crisp sets, 2nd class subsets are proper rough sets, and there are no 3rd class subsets in topological spaces generated by approximations. Also the important results about these spaces is that they are extremally disconnected [15], hence lattices of their domains are Boolean. Furthermore, we develop the theory of abstract spaces equipped with maps possessing characteristic properties of rough approximations which enables us to freely use the notions from the theory of rough sets and topological spaces formalized in the Mizar Mathematical Library [10].
3
Content available remote On almost (γ,γ’)-(β,β’)-s-continuous functions
80%
Rajesh N. , Vijayabharathi V.
Fasciculi Mathematici
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2014
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tom Nr 52
131--138
EN
The aim of this paper is to introduce and study a new class of functions called almost (γ,γ’)-(β,β’)-s-continuous functions in topological spaces by using (γ,γ’)-semiopen sets.
4
Content available remote Quasi δ-β-continuous functions
80%
Rajesh N. , Caldas M. , Jafari S. , Moshokoa S. P.
Fasciculi Mathematici
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2011
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tom Nr 46
105--113
EN
The aim of this paper is to introduce and characterize a new class of functions called quasi-δ-β-continuous functions in ideal topological spaces by using δ-β-open sets.
5
Content available remote More on almost contra λ-continuous functions
80%
Baker C. W. , Caldas M. , Jafari S. , Moshokoa S. P.
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tom Nr 42
17-28
EN
In 1996, Dontchev [14] introduced and investigated a new notion of non-continuity called contra-continuity. Recently, Baker et al. [6] offered a new generalization of contra-continuous functions via λ-closed sets, called almost contra λ-continuous functions. It is the objective of this paper to further study some more properties of such functions.
6
Content available remote On a class of (γ , γ')-preopen sets in a topological space
80%
Carpintero C. , Rajesh N. , Rosas E.
Fasciculi Mathematici
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2011
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tom Nr 46
25--35
EN
In this paper we have introduced the concept of (y, y')-preopen sets in topological space.
7
Content available remote Properties of ω-continuous functions
80%
Rajesh N. , Sudha P.
Fasciculi Mathematici
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2015
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tom Nr 55
171--182
EN
In [9] the authors, introduced the notion of ω-continuity and investigated its fundamental properties. In this paper, we investigate some more properties of this type of continuity.
8
Content available remote Graph quasi-continuity
80%
Mikucka A.
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2003
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tom Vol. 36, nr 2
483--494
9
Content available remote On semi δs-irresolute functions
70%
Caldas M. , Jafari S.
Fasciculi Mathematici
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2017
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tom Nr 58
47--55
EN
The concept of semi δs-irresolute function in topological spaces is introduced and studied. Some of their characteristic properties are considered. Also we investigate the relationships between these classes of functions and other classes of noncontinuous functions.
10
Content available remote On weakly g-continuous functions
70%
Rajesh N.
Fasciculi Mathematici
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2012
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tom Nr 48
97--103
EN
In this paper, we introduce a new class of functions called weakly g-continuous functions and investigate some of their fundamental properties.
11
Content available remote Efficient Computation of the Large Inductive Dimension Using Order- and Graph-theoretic Means
70%
Berghammer R. , Schnoor H. , Winter M.
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tom Vol. 177, nr 2
95--113
EN
Finite topological spaces and their dimensions have many applications in computer science, e.g., in digital topology, computer graphics and the analysis and synthesis of digital images. Georgiou et. al. [11] provided a polynomial algorithm for computing the covering dimension dim (X, 𝒯 ) of a finite topological space (X, 𝒯 ). In addition, they asked whether algorithms of the same complexity for computing the small inductive dimension ind (X, 𝒯 ) and the large inductive dimension Ind (X, 𝒯 ) can be developed. The first problem was solved in a previous paper [4]. Using results of the that paper, we also solve the second problem in this paper. We present a polynomial algorithm for Ind (X, 𝒯 ), so that there are now efficient algorithms for the three most important notions of a dimension in topology. Our solution reduces the computation of Ind (X, 𝒯 ), where the specialisation pre-order of (X, 𝒯 ) is taken as input, to the computation of the maximal height of a specific class of directed binary trees within the partially ordered set. For the latter an efficient algorithm is presented that is based on order- and graph-theoretic ideas. Also refinements and variants of the algorithm are discussed.
12
Content available remote Weak and strong forms of γ-irresoluteness
70%
Nasef A. A. , El-Maghrabi A. I.
Fasciculi Mathematici
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2013
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tom Nr 50
91--100
EN
In this paper we consider new weak and strong forms of y-irresoluteness and y-closure via the concept of gy-closed sets which we call ap-y-irresolute, ap-y-closed and contra-y-irresolute maps. Moreover, we use ap-y-irresolute and ap-y-closed maps to obtain a characterization of y — T1/2 -spaces.
13
Content available remote On gamma alfa-continuous functions
70%
Ekici E. , Noiri T.
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2005
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tom Vol. 38, nr 4
943--951
EN
The aim of this paper is to introduce and study gamma alfa-continuous functions as a generalization of preirresoluteness, alfa-precontinuity, alfa-irresoluteness, gamma-irresoluteness, irresoluteness and semi alfa-irresoluteness. Furthermore, basic characterizations, preservation theorems and several properties concerning gamma alfa-continuous functions are investigated. The relationships between gamma alfa-continuous functions and the other types of continuity are also discussed.
14
Content available remote On separated sets and connected spaces
60%
Ekici E.
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2007
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tom Vol. 40, nr 1
209-217
EN
The aim of this paper is to introduce the concept of connected topolog- ical spaces. Furthermore, the notions of separated sets, connected sets, component are introduced and studied. Also, the concept of set connectedness and connected spaces between subsets are introduced and the relationships of them are investigated.
15
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
60%
Noiri T. , Popa V.
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2005
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tom Vol. 38, nr 1
223--234
EN
In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
16
Content available On upper and lower strong quasi-uniform convergence of multivalued maps
60%
Dominik I. , Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2012
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tom Vol. 17
25-35
EN
The concept of strong convergence of functions and multifunctions was introduced by I. Kupka, V. Toma and A. Sochaczewska. In this paper we consider new definitions of convergence for the nets of multifunctions – upper and lower strong quasi-uniform convergence.
17
Content available remote K-differential spaces as sheaves. Induced and coinduced structure
60%
Piątkowski A.
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2005
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tom Vol. 38, nr 2
495--506
EN
Any K-differential space determines the sheaf of germs of its elements. We consider the K-differential space induced and coinduced by a single mapping. In this special case, we compare the sheaf of germs of the induced K-differential space with the inverse image of the sheaf of germs of a given K-differential space, and the sheaf of germs of the coinduced K-differential space with the image of the sheaf of germs of a given K-differential space.
18
Content available remote On maps and generalized lambda alfa-sets
60%
Caldas M. , Ganster M. , Jafari S. , Navalagi G. B.
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2005
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tom Vol. 38, nr 3
729--738
EN
In this paper we introduce and study the concepts of g-lambda alfa-continuous maps, g-lambda alfa-irresolute maps and g-lambda alfa-closed maps by using generalized lambda alfa-sets and generalized Valfa-sets.
19
Content available remote Combinatorial Geometry and Coding Theory
60%
Raigorodskii A. M.
Fundamenta Informaticae
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2016
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tom Vol. 145, nr 3
359--369
EN
In this paper, we overview three closely related problems: Nelson-Hadwiger problem on coloring spaces with forbidden monochromatics distances; Borsuk's problem on partitioning sets in spaces into parts of smaller diameter; problem of finding codes with forbidden Hamming distances.
20
Content available remote On an extension for functions
60%
Ekici E.
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2006
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tom Vol. 39, nr 3
657-670
EN
A new classes of functions, called strongly na-precontinuous functions, strongly na-continuous functions and na-continuous functions have been introduced. This paper considers the class of sigmas -na-continuous functions and its relationships to semi-regularization topologies, the other related functions. Preservation of appropriate topo-logical properties by sigmas -na-continuous functions is investigated.
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