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Contra-continuous functions and strongly S -closed spaces

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  • J. Dontchev

Abstract

In 1989 Ganster and Reilly [6] introduced and studied the notion of L C -continuous functions via the concept of locally closed sets. In this paper we consider a stronger form of L C -continuity called contra-continuity. We call a function f : ( X , τ ) → ( Y , σ ) contra-continuous if the preimage of every open set is closed. A space ( X , τ ) is called strongly S -closed if it has a finite dense subset or equivalently if every cover of ( X , τ ) by closed sets has a finite subcover. We prove that contra-continuous images of strongly S -closed spaces are compact as well as that contra-continuous, β -continuous images of S -closed spaces are also compact. We show that every strongly S -closed space satisfies FCC and hence is nearly compact.

Suggested Citation

  • J. Dontchev, 1996. "Contra-continuous functions and strongly S -closed spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:953839
    DOI: 10.1155/S0161171296000427
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    Cited by:

    1. Kocaman, A.H. & Yuksel, S. & Acikgoz, A., 2009. "On some strongly functions defined by α-open," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1346-1355.
    2. Ekici, Erdal, 2008. "On contra πg-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 71-81.
    3. Akdagˇ, Metin, 2007. "Weak and strong forms of continuity of multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1337-1344.
    4. Caldas, Miguel & Jafari, Saeid & Noiri, Takashi & Simões, Marilda, 2007. "A new generalization of contra-continuity via Levine’s g-closed sets," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1597-1603.
    5. Ekici, Erdal, 2008. "On (LC,s)-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 430-438.

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