• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.725-729
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• 2009

In this paper, we introduce the concepts of intuitionistic fuzzy generalized topological spaces and intuitionistic gradation of generalized openness. We also introduce the concepts of IFG-mapping, weak IFG-mapping and IFG-open mapping, and obtain some characterizations for such mappings.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.479-484
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• 2023

In this paper, we introduce the concept of a generalized derived set in generalized topological spaces and we investigate its properties. Using these, we study T_D-spaces in generalized topological spaces.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.619-624
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• 2010

We introduce the notions of bigeneralized topological spaces and quasi generalized open sets, and study some basic properties for the sets. We also introduce the notion of quasi generalized continuity on bigeneralized topological spaces, and investigate characterizations for the continuity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.305-320
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• 2013

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.243-254
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• 2022

In this paper, we introduce three different concepts of closed sets on the intuitionistic fuzzy topological spaces, i.e., the generalized fuzzy (r, s)-closed, semi-generalized fuzzy (r, s)-closed, and generalized fuzzy (r, s)-semiclosed sets on intuitionistic fuzzy topological spaces in Šostak's sense. Also we investigate their properties and the relationships among these generalized fuzzy closed sets.

• East Asian mathematical journal
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• v.23 no.2
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• pp.213-227
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• 2007

In this paper the concept of fuzzy nearly C-compactness is introduced in Generalized fuzzy topological spaces. Several characterizations and some interesting properties of these spaces in Generalized fuzzy topological spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions in Generalized fuzzy topological spaces are also studied.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.77-83
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• 2004

A class of topological algebras, which we call it a fundamental one, has already been introduced generalizing the famous Cohen factorization theorem to more general topological algebras. To prove the generalized versions of Cohen's theorem to locally multilplicatively convex algebras, and finally to fundamental topological algebras, the completness of the background spaces is one of the main conditions. The local convexity of the completion of a locally convex space is a well known fact and here we have a discussion on the completness of fundamental metrizable topological vector spaces.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.409-415
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• 2011

We introduce the notion of weakly quasi generalized continuous functions, and investigate properties for the continuity.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.404-407
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• 2009

In this paper, we introduce the concept of fuzzy generalized topologies which are generalizations of smooth topologies and Chang's fuzzy topologies and obtain some basic properties of their structure. Also we introduce and study the concepts of fuzzy generalized continuity and weakly fuzzy generalized continuity.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.387-399
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• 2014

We show that in quasi-topological spaces, separation axiom $T_2$ is equivalent to ${\alpha}-T_2$, $T_0$ is equivalent to semi - $T_0$, and semi - $T_{\frac{1}{2}}$ is equivalent to semi - $T_D$. Also, we give characterizations for ${\alpha}-T_1$, semi - $T_1$ and semi - $T_{\frac{1}{2}}$ generalized topological spaces.