Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Properties of Topological Ideals and Banach Category Theorem

  • Devi, V. Renuka (Department of Mathematics, Govindammal Aditanar College) ;
  • Sivaraj, D. (Department of Mathematics, Aditanar College) ;
  • Chelvam, T. Tamizh (Department of Mathematics, M. S. University)
  • Received : 2004.02.13
  • Published : 2005.06.23
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Abstract

An ideal space is ${\cal{I}}-resolvable$ if it has two disjoint ${\cal{I}}-dense$ subsets. We answer the question: If X is ${\cal{I}}-resolvable$, then is X (${\cal{I}}\;{\cup}\;{\cal{N}$)-resolvable?, posed by Dontchev, Ganster and Rose. We give three generalizations of the well known Banach Category Theorem and deduce the Banach category Theorem as a corollary. Characterizations of completely codense ideals and ${\cal{I}-locally$ closed sets are given and their properties are discussed.

Keywords

References

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