The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 10 Issue 1
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- Pages.25-35
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- 2003
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
REFLECTIONS OF COMPLETELY REGULAR AND ZERO-DIMENSIONAL QUASI-ORDERED SPACES
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