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ON $P-\mathcal{I}$-OPEN SETS

  • Kang, Jeong-Gi (Department of Mathematics Education Gyeongsang National University) ;
  • Kim, Chang-Su (Department of Mathematics Education Gyeongsang National University)
  • Received : 2009.04.08
  • Accepted : 2009.07.13
  • Published : 2009.09.25

Abstract

The notions of pre-local function, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of $P-\mathcal{I}$-open sets and $P-\mathcal{I}$-closed sets in ideal topological spaces are discussed. Relations between $\mathcal{I}$-open sets and $P-\mathcal{I}$-open sets are provided, and several properties related to $P-\mathcal{I}$-open sets, pre-local functions, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are investigated.

Keywords

Ideal topological spaces;pre-local (semi-local, ${\alpha}$-local) functions with respect to a topology and an ideal;P-I-open (closed) sets

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