REGULARLY QUASI-ORDERED SPACES AND NORMALLY QUASI-ORDERED SPACES

Abstract

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by T0-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.

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