Characterizing meager paratopological groups

Abstract

We prove that a Hausdorff paratopological group G is meager if and only if there are a nowhere dense subset A ⊂ G and a countable set C ⊂ G such that CA = G = AC.2010 MSC: 22A05, 22A30.

Descriptive Complexity of the Sizes of Subsets of Groups

“…Using this combinatorial characterization and the tree technique from [10], we can prove that the ideal of scattered subsets of a countable group G is coanalytic in P G . [17], every meager topological group G can be represented as the product G = CN of some countable subset C and nowhere dense subset N . Every infinite group G can be represented as a union of some countable family of small subsets [3].…”

“…4. By [17], every meager topological group G can be represented as the product G = CN of some countable subset C and nowhere dense subset N . Every infinite group G can be represented as a union of some countable family of small subsets [3].…”

Some properties of Pre-topological groups

“…x → x −1 , is also continuous. The the properties of topological groups have been widely used in the study of topology, analysis and category, see [1,2,4,27,28,29,30,31,32,38,39]. For more details about topological groups, the reader see [3].…”