On the topology of free paratopological groups. II

详细信息    查看全文

• 作者：Ali Sayed Elfard ; ^{ae351@uow.edu.au} ; ^{a.elfard@yahoo.com} ; Peter Nickolas ^{peter@uow.edu.au}
• 关键词：primary ; 22A30 ; secondary ; 54D10 ; 54E99 ; 54H99
• 刊名：Topology and its Applications
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：160
• 期：1
• 页码：220-229
• 全文大小：232 K

文摘

Let be the free paratopological group on a topological space X. For , denote by the subset of consisting of all words of reduced length at most n, and by the natural mapping from to . In this paper a neighbourhood base at the identity e in is found. A number of characterisations are then given of the circumstances under which the natural mapping is a quotient mapping, where X is a space and denotes the set equipped with the discrete topology. Further characterisations are given in the case where X is a transitive space. Several specific spaces and classes of spaces are also examined. For example, is a quotient mapping for every countable subspace of , is not a quotient mapping for any uncountable compact subspace of , and it is undecidable in ZFC whether an uncountable subspace of exists for which is a quotient mapping.