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Embeddings of biuniform spaces into topological groups

✍ Scribed by Michael G. Tkačenko

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
525 KB
Volume
77
Category
Article
ISSN
0166-8641

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✦ Synopsis

Given a completely regular space X with two uniformities b/I and/-/r both generating the original topology of X, we consider the question wbeth~ there exists a Hausdofff topological group G comaining X as a subspace such that *Vlx = b/~ and V* Ix = b/r, where *~ and ~;* are respectively the left and right group uniformities of G. We show that in general the answer is in the negative and present certain conditions implying the existence of an embedding of X to a topological group with the above properties. This approach enables us to conclude thai the difference between the left and right indices of boundedness for subsets of a topological group can. he arbitrary large.

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