REGULAR GLOSED BOOLEAN ALGBRA IN THE SPACE WITH EXTENSION TOPOLOGY

Cao, Shangmin; Cao, Shangmin

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P-ISSN3059-0604
E-ISSN3059-1309
KCI

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ISSN : 3059-0604

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Vol.7 No.2

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REGULAR GLOSED BOOLEAN ALGBRA IN THE SPACE WITH EXTENSION TOPOLOGY

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2000, v.7 no.2, pp.71-78

Cao, Shangmin (DEPARTMENT OF MATHEATICS, LIAOCHENG TEACHERS UNIVERSITY)

Cao, Shangmin. (2000). REGULAR GLOSED BOOLEAN ALGBRA IN THE SPACE WITH EXTENSION TOPOLOGY, 7(2), 71-78.

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Abstract

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

keywords: closed extension topogy, open extension topology, regular closed Booolean alebra, retration regular closed function, atom

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Vol.7 No.2

REGULAR GLOSED BOOLEAN ALGBRA IN THE SPACE WITH EXTENSION TOPOLOGY

Abstract

한국수학교육학회지시리즈B:순수및응용수학