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ISSN : 1226-0657

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Vol.10 No.1

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REFLECTIONS OF COMPLETELY REGULAR ANDZERO-DIMENSIONAL QUASI-ORDERED SPACES

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
2003, v.10 no.1, pp.25-35
Shin, Seon-Ho
Shin,, S. (2003). REFLECTIONS OF COMPLETELY REGULAR ANDZERO-DIMENSIONAL QUASI-ORDERED SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 10(1), 25-35.

Abstract

We study equivalent definitions and some categorical properties of completely regular quasi-ordered spaces and zero-dimensional quasi-ordered spaces. Using the o-completely regular (resp. o-zero-dimensional) filters on a completely regular (resp. zero-dimensional) quasi-ordered space, we show that the category COMPOS (resp. ZCOMPOS) of compact (resp. compact zero-dimensional) partially ordered spaces is reflective in the category CRQOS (resp. ZQOS) of completely regular (resp. zero-dimensional) quasi-ordered spaces and continuous isotones.

keywords
completely regular quasi-ordered spaces, zero-dimensional quasi-ordered spaces, o-completely regular filters, o-zero-dimensional filters, reflection, an universal initial completion, MacNeill completion, compact partially ordered spaces, compact zero-dimensional partially ordered spaces

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

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