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Embedding Paratopological Groups Into Topological Products by Mikhail Tkachenko is a Mathematics article available to read on EtoBox.

What is Embedding Paratopological Groups Into Topological Products about?

Hausdorff number Index of regularity Lindelöf number Second-countable First-countable Network Regular Hausdorff We show that a Hausdorff paratopological group G admits a topological embedding as a subgroup into a topological product of Hausdorff first-countable (second-countable) paratopological groups if and only if G is ω-balanced (totally ω-narrow) and the Hausdorff number of G is countable, i.e., for every neighbourhood U of the neutral element e of G there exists a countable family γ of neighbourhoods of e such that V ∈γ V V -1 ⊆ U . Similarly, we prove that a regular paratopological group G can be topologically embedded as a subgroup into a topological product of regular first-countable (second-countable) paratopological groups if and only if G is ω-balanced (totally ω-narrow) and the index of regularity of G is countable. As a by-product, we show that a regular totally ω-narrow paratopological group with countable index of regularity is Tychonoff.

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Author

Mikhail Tkachenko

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-8641)

Published

2009

Language

EN

Field

Mathematics (Physical Sciences)