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On subgroups of saturated or totally bounded paratopological groups

Show simple item record Banakh, Taras Ravsky, Sasha 2015-10-21T10:26:12Z 2015-10-21T10:26:12Z 2003
dc.description A paratopological group G is saturated if the in- verse U−1 of each non-empty set U ½ G has non-empty interior. It is shown that a [first-countable] paratopological group H is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if H admits a continuous bijective homomorphism onto a (totally bounded) [abelian] topological group G [such that for each neighborhood U ½ H of the unit e there is a closed subset F ½ G with e 2 h−1(F) ½ U]. As an application we construct a paratopological group whose character exceeds its ¼-weight as well as the character of its group reflexion. Also we present several ex- amples of (para)topological groups which are subgroups of totally bounded paratopological groups but fail to be subgroups of regular totally bounded paratopological groups. uk_UA
dc.language.iso en uk_UA
dc.publisher Луганский национальный университет им. Т. Шевченко uk_UA
dc.title On subgroups of saturated or totally bounded paratopological groups uk_UA
dc.type Article uk_UA

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    This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian and Russian mathematician, one of the founder of our journal Professor Rostislav Grigorchuk, who was 50 years of age on February 23, 2003.

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