• Title/Summary/Keyword: m-extremally disconnected

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ON EXTREMALLY DISCONNECTED SPACES VIA m-STRUCTURES

  • Al-Omari, Ahmad;Al-Saadi, Hanan;Noiri, Takashi
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.351-359
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    • 2019
  • In this paper, we introduce a modification of extremally disconnected spaces which is said to be m-extremally disconnected. And we obtain many characterizations of m-extremally disconnected spaces. The concepts of ${\ast}$-extremally disconnected spaces, ${\ast}$-hyperconnected spaces, and generalized hyperconnectedness are as examples for this paper.

TIETZE EXTENSION THEOREM FOR ORDERED FUZZY PRE-EXTREMALLY DISCONNECTED SPACES

  • Uma, M.K.;Roja, E.;Balasubramanian, G.
    • East Asian mathematical journal
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    • v.24 no.3
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    • pp.213-221
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    • 2008
  • In this paper, a new class of fuzzy topological spaces called ordered fuzzy pre-extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy pre-extremally disconnected spaces has been discussed as in [9] besides proving several other propositions and lemmas.

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[ $G_{\delta}$ ]-CONNECTEDNESS AND $G_{\delta}$-DISCONNECTEDNESS IN FUZZY BITOPOLOGICAL SPACES

  • Roja, E.;Uma, M.K.;Balasubramanian, G.
    • East Asian mathematical journal
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    • v.23 no.2
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    • pp.159-174
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    • 2007
  • In this paper, the concepts of pairwise fuzzy $G_{\delta}$-connected spaces and pairwise fuzzy $G_{\delta}$-extremally disconnected spaces are introduced. The concept of pairwise fuzzy $G_{\delta}$-basically disconnected spaces is defined. Characterizations of the above spaces are given besides giving several examples. Interrelations among the spaces introduced are discussed and some relevant counter examples are given.

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DECOMPOSITION OF CONTINUITY AND COMPLETE CONTINUITY IN SMOOTH FUZZY TOPOLOGICAL SPACES

  • Amudhambigai, B.;Uma, M.K.;Roja, E.
    • East Asian mathematical journal
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    • v.27 no.3
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    • pp.261-271
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    • 2011
  • In this paper, fuzzy ${\alpha}^*$-set, fuzzy C-set, fuzzy AB-set, fuzzy t-set, fuzzy B-set, etc., are introduced in the sense of Sostak [12] and Ramadan [9]. By using these sets, a decomposition of fuzzy continuity and complete fuzzy continuity are provided. Characterization of smooth fuzzy extremally disconnected spaces is also obtained in this connection.