• Communications of the Korean Mathematical Society
• /
• v.30 no.4
• /
• pp.385-402
• /
• 2015

In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of "$c_f$-Max X", we prove that every member of "$c_f$-Max X" is a prime ideal. Also we conclude some more related results.

• Honam Mathematical Journal
• /
• v.29 no.3
• /
• pp.307-326
• /
• 2007

The aim of this paper is to introduce and study topological properties of semi-limit points, semi-derived, semi-interior, semi-closure, semi-border, and semi-frontier of a set using the concept of semi-open set.

• East Asian mathematical journal
• /
• v.23 no.1
• /
• pp.45-58
• /
• 2007

The notions of IVF strongly semiopen (semiclosed) sets and IVF (strong) semi-interior (IVF (strong) semi-closure) are introduced, and several examples are provided. Related properties are investigated. In particular, characterizations of an IVF strongly semiopen set are discussed.

• Kyungpook Mathematical Journal
• /
• v.54 no.2
• /
• pp.173-188
• /
• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• Kyungpook Mathematical Journal
• /
• v.54 no.2
• /
• pp.221-236
• /
• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.359-365
• /
• 1998

We give two sufficient conditions that the space (X,C*) be a Fr$\acute{e}$chet-Urysohn space such that $x_n \to x$ in (X,c) if and only if $x_n \to x$ in (X,c*), where c* is the sequential closure operator on a generalized topological (X,c).

• Journal of Industrial Technology
• /
• v.4
• /
• pp.25-27
• /
• 1984

위상 공간 X의 모든 Semi-open cover에 대하여 그들의 closure의 합이 X를 cover한 유한 부분 속이 존재할 때 위상 공간X를 S-closed라고 한다. 이 논문에서는 S-closed와 semi-closed set 사이의 관계를 조사하였고 Haussdorff 공간과 S-closed 공간에서 extremally disconnected와 semi-continuous의 성질을 조사하였다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1997.11a
• /
• pp.47-51
• /
• 1997

In this paper, certain fuzzy semi-separation axioms are studied in terms of the notions of quasi-coincidence, fuzzy semi-q-neigborhoods and fuzzy semi-$\theta$-closure operators. Fuzzy semi-T2, fuzzy semi-Urysohn and fuzzy s-regular spaces are defined, and fuzzy spaces satisfying these axioms are characterized.

• Communications of the Korean Mathematical Society
• /
• v.17 no.3
• /
• pp.531-534
• /
• 2002

We prove that the star operator and the sequential closure operator on a weakly first countable space are the same and show that the Frechetness is a sufficient condition for a weakly first countable space to be first countable.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2005.11a
• /
• pp.209-212
• /
• 2005

In this paper, we introduce the concept of fuzzy quasi extremally disconnectedness in fuzzy bitopological space, which is a generalization of fuzzy extremally disconnectedness due to Ghosh [5] in fuzzy topological space and investigate some of its properties using the concepts of quasi-semi-closure, quasi-$\Theta$_closure and related notions in a fuzzy bitopological setting.