When a compact (countably compact) set is closed. II |
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Authors: | L. Garg Navpreet Singh |
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Affiliation: | (1) Department of Mathematics, Punjabi University Patiala-, 147002 India E-mail |
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Abstract: | We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T4,-spaces. |
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Keywords: | compact countably compact closed normal sequence net cluster point T4 product subspace sequential quotient Fré chet limit |
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