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1
Content available remote New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations
Al-shami Tareq M., Tercan Adnan, Mhemdi Abdelwaheb
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
196--211
EN
In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely tt-soft pre Ti (i = 0, 1, 2, 3, 4) and tt-soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre Ti (i = 0, 1, 2, 3, 4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a tt-soft pre-regular space and demonstrate that it guarantees the equivalence of tt-soft pre Ti (i = 0, 1, 2). Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of productand sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.
2
Content available remote On soft pc-separation axioms
Hamko Qumri H., Ahmed Nehmat K., Khalaf Alias B.
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
67--79
EN
Many mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological space X. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft pc−Ti and soft pc−T⁎i, i=0,1,2 by using the concept of soft pc-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.
3
Content available remote Applications of some operators on supra topological spaces
Asaad Baravan A., Al-shami Tareq M., Abo-Tabl El-Sayed A.
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
292--308
EN
In this paper, the notion of an operator γ on a supra topological space(X, μ) is studied and then utilized to analyze supra γ-open sets. The notions of μγ-g. closed sets on the subspace are introduced and investigated. Furthermore, some new μγ-separation axioms are formulated and the relationships between them are shown. Moreover, some characterizations of the new functions via operator γ on μ are presented and investigated. Finally, we give some properties of S(γ, β)-closed graph and strongly S(γ, β)-closed graph.
4
Content available On upper and lower strong quasi-uniform convergence of multivalued maps
Dominik I., Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2012
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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.
5
Content available remote On separated sets and connected spaces
Ekici E.
Demonstratio Mathematica
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2007
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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.
6
Content available remote On an extension for functions
Ekici E.
Demonstratio Mathematica
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2006
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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.
7
Content available remote A note on the graph continuity
Przemski M.
Demonstratio Mathematica
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2006
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Vol. 39, nr 4
927-937
EN
The aim of this paper is to presented and study the concept of local version of the relationship between the graphs and the closure of the graphs for pairs of functions. Some characterisations of certain generalized forms of continuity are also obtained.
8
Content available remote On gamma alfa-continuous functions
Ekici E., Noiri T.
Demonstratio Mathematica
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2005
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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.
9
Content available remote Graph quasi-continuity
Mikucka A.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
483--494
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