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Weakly clopen functions

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  • Son, Mi Jung
  • Park, Jin Han
  • Lim, Ki Moon

Abstract

We introduce a new class of functions called weakly clopen function which includes the class of almost clopen functions due to Ekici [Ekici E. Generalization of perfectly continuous, regular set-connected and clopen functions. Acta Math Hungar 2005;107:193–206] and is included in the class of weakly continuous functions due to Levine [Levine N. A decomposition of continuity in topological spaces. Am Math Mon 1961;68:44–6]. Some characterizations and several properties concerning weakly clopenness are obtained. Furthermore, relationships among weak clopenness, almost clopenness, clopenness and weak continuity are investigated.

Suggested Citation

  • Son, Mi Jung & Park, Jin Han & Lim, Ki Moon, 2007. "Weakly clopen functions," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1746-1755.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:5:p:1746-1755
    DOI: 10.1016/j.chaos.2006.03.026
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    References listed on IDEAS

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    1. D. A. Rose, 1984. "Weak continuity and strongly closed sets," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-8, January.
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    Cited by:

    1. Ekici, Erdal, 2008. "Generalization of weakly clopen and strongly θ-b-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 79-88.
    2. Ekici, Erdal, 2009. "A note on almost β-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1010-1013.

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