Prime subspaces in free topological groups

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• 作者：Eda ; Katsuya ; Ohta ; Haruto ; Yamada ; Kohzo
• 关键词：Free topological group ; Free Abelian topological group ; Symmetric product ; Prime space ; Self-embeddable space ; Convergent sequence ; 54B10 ; 22A99 ; 20E05
• 刊名：Topology and its Applications
• 出版年：1995
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：March 24, 1995
• 卷：62
• 期：2
• 页码：163-171
• 文件大小：465 K

摘要

Let F (X) (A(X)) be the free (Abelian) topological group over X. We prove: If P is one of the spaces R, Q, R \ Q, βω, βω \ ω and 2^κ for an infinite κ and ifF (X) or A(X) contains a copy of P, then X contains a copy of P. If P is the one-point compactification of an infinite discrete space or ω₁ + 1, this is not true. If P = ω₁, this holds for F(X) but is independent of ZFC for A(X).