scholarly journals Countably compact groups and finest totally bounded topologies

1973 ◽  
Vol 49 (1) ◽  
pp. 33-44 ◽  
Author(s):  
W. Wistar Comfort ◽  
Victor Saks
Keyword(s):  
Compact Groups ◽  
Totally Bounded ◽  
Countably Compact

scholarly journals Countably compact groups without non-trivial convergent sequences

2020 ◽  
Vol 374 (2) ◽  
pp. 1277-1296 ◽  
Author(s):  
M. Hrušák ◽  
J. van Mill ◽  
U. A. Ramos-García ◽  
S. Shelah
Keyword(s):  
Compact Groups ◽  
Countably Compact ◽  
Convergent Sequences

A generalization of isometries to uniform spaces

1956 ◽  
Vol 52 (3) ◽  
pp. 399-405 ◽  
Author(s):  
F. Rhodes
Keyword(s):  
Metric Spaces ◽  
Uniform Space ◽  
Compact Groups ◽  
Uniform Spaces ◽  
Totally Bounded ◽  
Transitive Groups ◽  
Groups Of Automorphisms

Isomorphisms are, in many ways, the generalizations of isometrics to uniform spaces. Yet some theorems on isometries of metric spaces only generalize to uniform spaces in terms of more restricted transformations of the uniform space. In § 1, in the course of a discussion of a theorem on transitive groups of automorphisms, we define such a transformation and call it an isobasism. It appears that in many respects isobasisms, rather than isomorphisms, are the generalizations of isometries to uniform spaces. The results of Freudenthal and Hurewicz (7) on contractions, expansions and isometries of totally bounded metric spaces are generalized, in § 2, to contractions, expansions and isobasisms of totally bounded uniform spaces. These results, together with generalizations of some theorems of Eilenberg (6) on compact groups of homeomorphisms of metric spaces which are obtained in §3, give a characterization of isobasisms. The language of Bourbaki (2,3,4) is used throughout this note.

scholarly journals Countably compact groups and sequential order

2020 ◽  
Vol 270 ◽  
pp. 106943 ◽  
Author(s):  
Dmitri Shakhmatov ◽  
Alexander Shibakov
Keyword(s):  
Compact Groups ◽  
Sequential Order ◽  
Countably Compact

scholarly journals Topological properties of the scale of a uniform space

1982 ◽  
Vol 33 (1) ◽  
pp. 54-61 ◽  
Author(s):  
G. D. Richardson ◽  
E. M. Wolf
Keyword(s):  
Uniform Space ◽  
Topological Properties ◽  
Uniform Lattice ◽  
Totally Bounded ◽  
Countably Compact

AbstractLet (S. U) be a uniform space. This space can be embedded in a complete, uniform lattice called the scale of (S. U). We prove that the scale is compact if and only if S is finite or U = {S × S}. We prove that this statement remains true if compact is replaced by countably compact, totally bounded. Lindelof, second countable, or separable. In the last section of this paper, we investigate the cardinality of the scale and the retracted scale.

scholarly journals Countably compact groups from a selective ultrafilter

2004 ◽  
Vol 133 (3) ◽  
pp. 937-943 ◽  
Author(s):  
S. Garcia-Ferreira ◽  
A. H. Tomita ◽  
S. Watson
Keyword(s):  
Compact Groups ◽  
Countably Compact ◽  
Selective Ultrafilter
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