REGULAR CLOSED BOOLEAN ALGEBRA IN SPACE WITH ONE POINT LINDELOFFICATION TOPOLOGY

Gao, Shang-Min; Gao, Shang-Min

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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ISSN : 1226-0657

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Vol.7 No.1

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2000, v.7 no.1, pp.61-69

Gao, Shang-Min

Gao,, S. (2000). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 7(1), 61-69.

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Abstract

Let(<TEX>$X^{\ast},\tau^{\ast}$</TEX>) be the space with one point Lindeloffication topology of space (X,<TEX>$\tau$</TEX>). This paper offers the definition of the space with one point Lin-deloffication topology of a topological space and proves that the retraction regu-lar closed function f: <TEX>$K^{\ast}(X^{\ast}$</TEX>) defined f(<TEX>$A^{\ast})=A^{\ast}$</TEX> if p <TEX>$\in A^{\ast}$</TEX> or (<TEX>$f(A^{\ast})=A^{\ast}-{p}$</TEX> if <TEX>$p \in A^{\ast}$</TEX> is a homomorphism. There are two examples in this paper to show that the retraction regular closed function f is neither a surjection nor an injection.

keywords: one point Lindeloffication topolgy, regular closed Boolean algebran, retraction regular closed function, half-disc topology

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Article Contents

Vol.7 No.1

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics