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

• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.455-465
• /
• 2016

The number of topologies on a finite set is a famous open problem. In the present paper we discuss a method of obtaining the number of generalized topologies on finite sets.

• Communications of the Korean Mathematical Society
• /
• v.28 no.4
• /
• pp.819-825
• /
• 2013

Similarly to Tychonoff product, we introduce the concept of generalized product topology which is different from the notion of product of generalized topologies in [$\acute{A}$. $Cs\acute{a}sz\acute{a}r$, Acta Math. Hungar. 123 (2009), 127-132] for generalized topology and obtain some properties about it. Besides, we prove that connectedness, ${\sigma}$-connectedness and ${\alpha}$-connectedness are all preserved under this product.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.315-330
• /
• 1998

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $R^{2＋p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $R_{p}$ $^{2＋p}$ with 1-type generalized Gauss map.p.

• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.325-340
• /
• 2003

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

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

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.415-424
• /
• 2012

As a generalization of countably approximating posets, we introduce the concept of generalized countably approximating posets. Some properties of generalized countably approximating posets are presented.

• The Pure and Applied Mathematics
• /
• v.14 no.4
• /
• pp.255-270
• /
• 2007

In this paper, we introduce the concepts of r-generalized fuzzy closed sets, r-generalized fuzzy continuous maps and several types of r-generalized compactness in fuzzy topological spaces and investigate some of their properties.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.1
• /
• pp.183-191
• /
• 2018

This paper deals with binary ideal topological space and discuss about generalized binary closed sets and generalized kernel in the same topological space. Further it will discuss various types of characterizations of generalized binary closed sets and generalized kernel.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.20 no.6
• /
• pp.848-851
• /
• 2010

In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.