• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.119-130
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• 2006

A new class of functions is introduced in this paper. This class is called almost ${\delta}$-precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using ${\delta}$-preopen sets, many characterizations and properties of the said type of functions are investigated.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.589-596
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• 2013

This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.199-203
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• 2010

We introduce the notions of sg-semiopen set and other kinds of generalized sg-open sets and we investigate some properties for such generalized sg-open sets.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.135-149
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• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.