• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.5
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• pp.614-620
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• 2003

The aim of this paper is to introduce good definitions of compactness, almost compactness, near compactness, weak compactness, and S-closedness in fuzzy topological spaces in Sostak s sense. These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studied.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.291-300
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• 2008

In this paper, we introduce several types of r-semi-generalized fuzzy compactness and fuzzy r-compactness in fuzzy topological spaces and investigate the relations between these compactness.

• The Pure and Applied Mathematics
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• v.11 no.3
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• pp.217-229
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• 2004

In this paper, we introduce the concepts of interior of a fuzzy set and several types of fuzzy compactness and fuzzy RS-compactness in a redefined fuzzy topological space and investigate their properties.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.249-254
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• 2005

In this paper, we introduce the concepts of intuitionistic fuzzy half-compactness, nearly intuitionistic fuzzy half-compactness and almost intuitionistic fuzzy half-compactness defined by intuitionistic gradations of openness, and obtain some characterizations.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.581-590
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• 2014

In approach theory, we can provide arbitrary products of ${\infty}p$-metric spaces with a natural structure, whereas, classically only if we rely on a countable product and the question arises, then, whether properties which are derived from countability properties in metric spaces, such as sequential and countable compactness, can also do away with countability. The classical results which simplify the study of compactness in pseudometric spaces, which proves that all three of the main kinds of compactness are identical, suggest a further study of the category $pMET^{\infty}$.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.63-70
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• 2007

In this paper, we introduce the concepts of r-gp-open map, weakly r-gp-open map, intuitionistic fuzzy r-compactness, nearly intuitionistic fuzzy r-compactness and almost intuitionistic fuzzy r-compactness defined by intuitionixtic gradations of openness, and obtain some characterizations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.41-44
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• 2003

First, we investigate some properties of fuzzy compactness. Second, we introduce the concept of fuzzy local compactness in fuzzy topological space and study some of its properties. Finally, we investigate some relations between F-compactness in fuzzy topological spaces and one in fuzzy hyperspaces.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.493-499
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• 2008

We construct a minimizing sequence for the Sobolev trace inequality which satises compactness in the concentration compactness property.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.79-82
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• 1988

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.123-130
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• 1999

We characterize the compactness, weak precompactness and weak compactness in $L^P({\mu},X)$ and in more general space $P^c({\mu},X)$. Moreover, we present this characterization in terms of extremal structure in X.