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Locally closed sets and LC -continuous functions

Author

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  • M. Ganster
  • I. L. Reilly

Abstract

In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.

Suggested Citation

  • M. Ganster & I. L. Reilly, 1989. "Locally closed sets and LC -continuous functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:758376
    DOI: 10.1155/S0161171289000505
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    Cited by:

    1. Ekici, Erdal, 2008. "On locally closedness and continuity," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1244-1255.
    2. 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.
    3. Ekici, Erdal, 2008. "On (LC,s)-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 430-438.
    4. Ekici, Erdal, 2008. "On contra πg-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 71-81.
    5. Keskin, Aynur & Noiri, Takashi, 2009. "Almost contra-g-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 238-246.
    6. Ekici, Erdal & Noiri, Takashi, 2009. "Decompositions of continuity, α-continuity and AB-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2055-2061.

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