논문KCI 등재
CLOZ-COVERS OF TYCHONOFF SPACES
한국수학교육학회|2011.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제18권 제4호|pp. 361-368
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초록
In this paper, we construct a cover (L(X); cX) of a space X such that for any cloz-cover (Y; f) of X, there is a covering map g : Y ¡! L(X) with cX ± g =f. Using this, we show that every Tychono® space X has a minimal cloz-cover (Ecc(X); zX) and that for a strongly zero-dimensional space X, ¯Ecc(X) = Ecc(¯X) if and only if Ecc(X) is z#-embedded in Ecc(¯X).
Abstract
In this paper, we construct a cover (L(X); cX) of a space X such that for any cloz-cover (Y; f) of X, there is a covering map g : Y ¡! L(X) with cX ± g =f. Using this, we show that every Tychono® space X has a minimal cloz-cover (Ecc(X); zX) and that for a strongly zero-dimensional space X, ¯Ecc(X) = Ecc(¯X) if and only if Ecc(X) is z#-embedded in Ecc(¯X).
참고문헌 (8)
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- M. Henriksen, "Wallman covers of compact spaces", Dissertationes Mathematicae 283, 283, pp.5~31 (1989)
- S. Iliadis, "Absolute of Hausdorff spaces", Sov. Math. Dokl, 4, pp.295~298 (1963)
- C.I. Kim, "Minimal Cloz-covers of non-compact spaces", J. Korean Soc. Math. Edu, 4, pp.151~159 (1997)
- J. Porter, "Extensions and Absolutes of Hausdorff Spaces" (1988), Springer
- J. Vermeer, "The smallest basically disconnected preimage of a space", Topol. Appl, 17, pp.217~232 (1984)
관련 논문AI추천
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