supfxcompactness family S of su (S. 1) every cover of x y elements of S as a two-elemen and ' (5.2) if SO U S1 = X = SO Lj S, with Si E S for i = 0, 1 9 2, t S, C S2 or Sz C S, (i.e., S, and S, are conaparable by inclusior!). 2.2. A topological space X is 2-cc0m~ct iff there exists an which genera
A topological characterization of ordered spaces
β Scribed by J. van Dalen; E. Wattel
- Publisher
- Elsevier Science
- Year
- 1973
- Weight
- 999 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0016-660X
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## Abstract Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the __T__~0~(__T__~1~,
In the hyperspace Exp X of all closed subsets of a topological space X interval and order topology solely use the c-relation in Exp X for their definitions whereas HAUSDORFB set convergence and VIETORIS topology use neighbourhoods in X itself. Nevertheless there exist intimate but non-trivial relati