• Title/Summary/Keyword: semi-closure space

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On a Class of γ*-pre-open Sets in Topological Spaces

  • Krishnan, G. Sai Sundara;Saravanakumar, D.;Ganster, M.;Ganster, M.
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.173-188
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    • 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.

On Soft Topological Space via Semiopen and Semiclosed Soft Sets

  • Mahanta, Juthika;Das, Pramod Kumar
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.221-236
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    • 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.

A note on S-closed space (S-closed 공간에 관하여)

  • Han, Chun-Ho
    • Journal of Industrial Technology
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    • v.4
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    • pp.25-27
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    • 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.

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Fuzzy quasi extremally disconnected spaces (퍼지 준 extremally disconnected 공간)

  • Park, Jin-Han;Park, Yong-Beom;Lee, Bu-Young
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.11a
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    • pp.209-212
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    • 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.

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QUASI-FUZZY EXTREMALLY DISCONNECTED SPACES

  • Lee, Bu-Young;Son, Mi-Jung;Park, Yong-Beom
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1998.10a
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    • pp.77-82
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    • 1998
  • In this paper, we introduce the concept of quasi-fuzzy extremally disconnectedness in fuzzy bitopological space, which is a generalization of fuzzy extremally disconnectedness due to Ghosh [5] in fuzzy topological space and invetstigate some of its properties using the concepts of quasi-semi-closure, quasi-$\theta$-closure and related notions in a fuzzy bitopological settings.

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ON SOFT REGULAR-OPEN(CLOSED) SETS IN SOFT TOPOLOGICAL SPACES

  • HUSSAIN, SABIR
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.59-68
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    • 2018
  • In this paper, We define and explore the characterizations and properties of soft regular open(closed) and soft semi-regular sets in soft topological spaces. The properties of soft extremally disconnected spaces are also introduced and discussed. The findings in this paper will help researcher to enhance and promote further study on soft topology to carry out a general framework for their applications in practical life.

ON SUPER CONTINUOUS FUNCTIONS

  • Baker, C.W.
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.17-22
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    • 1985
  • B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

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