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AN EXTENSION WHICH IS A WEAKLY LINDELÖFF SPACE

김창일|윤용식
한국수학교육학회|2012.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제19권 제3호|pp. 273-279|DOI http://dx.doi.org/

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참고문헌

키워드

filterrealcompactificationweakly LindelAÖff space.
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초록

In this paper, we construct an extension (kX; kX) of a space X such that kX is a weakly LindelÄo® space and for any continuous map f : X ¡! Y , there is a continuous map g : kX ¡! kY such that g jX= f. Moreover, we show that ÀX is LindelÄo® if and only if kX = ÀX and that for any P0-space X which is weakly LindelÖff, kX = ÀX.

Abstract

In this paper, we construct an extension (kX; kX) of a space X such that kX is a weakly LindelÄo® space and for any continuous map f : X ¡! Y , there is a continuous map g : kX ¡! kY such that g jX= f. Moreover, we show that ÀX is LindelÄo® if and only if kX = ÀX and that for any P0-space X which is weakly LindelÖff, kX = ÀX.

참고문헌 (6)

  1. J.L. Blasco, "Complete bases and Wallman realcompactications", Proc. Amer. Math. Soc, 75, pp.114~118 (1979)
  2. J.L. Blasco, "Complete bases in topological spaces II", Studia Sci. Math. Hung, 24, pp.447~452 (1989)
  3. L. Gillman, "Rings of continuous functions" (1960), Van Nostrand
  4. Chang Il Kim, "Almost P-spaces", 대한수학회논문집, 18(4), pp.695~701 (2003), 대한수학회
  5. J. Porter, "Extensions and Absolutes of Hausdorff Spaces" (1988), Springer
  6. A.I. Veksler, "P'-points, P'-sets, P'-spaces. A new class of order-continuous measures and functionals", Soviet Math. Dokl, 14, pp.1445~1450 (1973)

관련 논문AI추천

BASICALLY DISCONNECTED COVERS OF THE EXTENSION kX OF A SPACE X김창일영남수학회 · East Asian Mathematical Journal2013 · 제29권 제1호Minimal Basically Disconnected Covers of P'-spaces김창일, 정갑헌영남수학회 · East Asian Mathematical Journal2014 · 제30권 제1호MINIMAL BASICALLY DISCONNECTED COVER OF WEAKLY P-SPACES AND THEIR PRODUCTS김창일한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제2호CLOZ-COVERS OF TYCHONOFF SPACES김창일한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호REMARKS ON CS-STARCOMPACT SPACESYan-Kui Song대한수학회 · 대한수학회논문집2012 · 제27권 제1호ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT홍우철대한수학회 · 대한수학회논문집2010 · 제25권 제3호

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