CATEGORICAL PROPERTIES OF SEMI-CONTINUOUS QUASI-ORDERED SPACES Shin, Seon-Ho;
We study categorical properties of the category SWQOS (SU/WQOS, SL/WQOS, resp) of (upper, lower, resp.) semi-continuous quasi-ordered spaces and the subcategory SWPOS (SU/WPOS, SL/WPOS, resp.) of (upper, lower, resp.) semicontinuous partially ordered spaces. We show that the categories SU/WPOS, SL/WPOS and SWPOS are closed under the formation of initial mono-sources in the category TQOS of topological quasi-ordered spaces, and they we mono-topological, complete and cocomplete epireflective subcategories of the category TQOS. We obtain their MacNeille and universal initial completions, as well as those of subcatego.ies SU/WQOS(SL/WQOS) and SWQOS, in which the topologies are T0/ and T, respectively.
(upper, lower) semi-continuous quasi-ordered spaces;MacNeille and universal initial completions;
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