โ Scribed by J. de Groot; P.S. Schnare
No coin nor oath required. For personal study only.
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 generates t topology on J and is a 2-ccompact urbaki, but unljke elley, tie allogw S = 0 as a subbase for bus S = 0 is a 2-ccompa :t subbase fo hen we wish to make the 2-ccompact su /W Cl ic a 3-rCQmsp& space". \4*, J, 1" u " r/ 1 very 2-ccompact space is compact by (S. 1) and Alexander's subbase theorem.
Note that S and S @, X) generate the same topology, and ,Xj is 2-ccom act. 'vci, shall assume without nd X $ S . This convention eliminates some trivial cases ir?
๐ SIMILAR VOLUMES
## Abstract Compact metric spaces ฯ of such a kind, that ๐น~__f__~ =๐น(__X__), are characterized, ๐น(__X__) is the ฯโfield of BOREL sets and ๐น~__f__~(__X__) is the field generated by all open subset of __X__. Our main result is Theorem 5: If ฯ is a compact metric space, then the following conditions a
## 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~,