Continuity of the Inverse in Pseudocompact Paratopological Groups

• 来源期刊: 代数集刊（英文版）
• 关键词: C-compact bispace Stone-Cech bicompactification topological semigroup,paratopological group pseudocompact group
• 年，卷（期）: 2007,（1）
• 页码范围: 167-175
• 页数: 9页
• 语种: 英文

摘要

By a celebrated theorem of Numakura, a Hausdorff compact topological semi-group with two-sided cancellation is a group which has inverse continuous, I.e., it is atopological group. We improve Numakura's Theorem in the realm of non-Hausdorff topo-logical semigroups. This improvement together with some properties of pseudocompactnature in the field of bitopological spaces is used in order to prove that a To paratopological group (G, T) is a (Hausdorff) pseudocompact topological group if and only if (G,T V T -1)is pseudoco_ mpact or, equivalently, G is Gδ-dense in the Stone-Cech bicompactification (β2G,(∧T∧T-1) of(G,T,T- 1) of (G, T,T - 1). We also present a version for paratopological groups of the renowned Comfort-Ross Theorem stating that a topological group is pseud0compact if and only if its Stone-Cech compactification is a topological group.