• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.633-643
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• 2010

In this paper, the concept of maximal ideals relative to a filter on posets is introduced and examined. An intrinsic characterization of distributive lattices is obtained. In addition, we also give a characterization of pseudo primes in semicontinuous lattices and a characterization of semicontinuous lattices. Functions of semicontinuous lattices which are order preserving and semicontinuous are studied. A new concept of semiarithmetic lattices is introduced and examined.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.149-153
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• 2012

In this paper, we introduce the concept of fuzzy almost strongly (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy strongly (r, s)-semicontinuous, fuzzy almost (r, s)-continuous, fuzzy almost (r, s)-semicontinuous, and fuzzy almost strongly (r, s)-semicontinuous mappings are discussed. The characterization for the fuzzy almost strongly (r, s)-semicontinuous mappings is obtained.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.341-353
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• 2003

As a generalizaton of the concepts of fuzzy strongly semiopen sets and fuzzy strongly semicontinuous maps, we introduce the concepts of fuzzy strongly r-semiopen sets and fuzzy strongly r-semicontinuous maps in fuzzy topology. Also we introduce fuzzy r-semicontinuous and fuzzy r-semiclosure. By these concept, we characterize fuzzy strongly r-semicontinuous, fuzzy strongly r-semiopen and fuzzy strongly r-semiclosed maps.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.421-424
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• 2009

In this paper, we introduce the concept of fuzzy semi-weakly r-semicontinuous mappings on a fuzzy topological space and study characterizations for such mappings. And we investigate the relationships among fuzzy r-semicontinuity, fuzzy semi-weakly r-semicontinuity and fuzzy weakly r-semicontinuity.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.848-851
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• 2009

In [5], we introduced the concepts of IVF m-semiopen sets and IVF m-semicontinuous mappings on interval-valued fuzzy minimal spaces. In this paper, we investigate some properties of IVF m-semiopen sets and characterizations for the IVF m-semicontinuous mapping.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.254-258
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• 2011

In this paper, we introduce the notion of fuzzy (r, s)-S1-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense, which is a generalization of $S_1$-pre-semicontinuous mappings by Shi-Zhong Bai. The relationship between fuzzy (r, s)-pre-semicontinuous mapping and fuzzy (r, s)-$S_1$-pre-semicontinuous mapping is discussed. The characterizations for the fuzzy (r, s)-$S_1$-pre-semicontinuous mappings are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.187-199
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• 2009

In this paper, we introduce the concept of fuzzy weakly (r,s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among various kinds of fuzzy mappings on intuitionistic fuzzy topological spaces in $\check{S}ostak^{\prime}s$ sense are displayed. The characterization for the fuzzy weakly (r,s)-semicontinuous mapping is obtained. Also, we introduce the notion of fuzzy weakly (r,s)-semicontinuous mappings at a given intuitionistic fuzzy point. The relation between fuzzy weakly (r,s)- semicontinuous mappings and fuzzy weakly (r,s)-semicontinuous mappings at an intuitionistic fuzzy point is discussed.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.757-764
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• 2013

In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.189-200
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• 2006

The semicontinuous quasi-uniformity is known to be one of the most important examples of transitive quasi-uniformities. The aim of this paper is to show that various facts in classical topology connected with the semicontinuous quasi-uniformity and semicontinuous real functions may be easily extended to pointfree topology via a construction introduced by the authors in a previous paper. Several consequences are derived.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.239-245
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• 2009

In this paper, we introduce the notions of m-semiopen sets and M-semicontinuous functions on spaces with minimal structures and study some properties of such notions. In particular, we investigate characterizations for the M-semicontinuous function and the relationship between M-continuity and M-semicontinuity.