TY - JOUR
T1 - Prime subspaces in free topological groups
AU - Eda, Katsuya
AU - Ohta, Haruto
AU - Yamada, Kohzo
PY - 1995/3/24
Y1 - 1995/3/24
N2 - 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/gk for an infinite κ and if F(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 ZFCfor A(X).
AB - 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/gk for an infinite κ and if F(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 ZFCfor A(X).
KW - Convergent sequenc
KW - Free Abelian topological group
KW - Free topological group
KW - Prime space
KW - Self-embeddable space
KW - Symmetric product
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U2 - 10.1016/0166-8641(94)00030-7
DO - 10.1016/0166-8641(94)00030-7
M3 - Article
AN - SCOPUS:0037818767
SN - 0166-8641
VL - 62
SP - 163
EP - 171
JO - Topology and its Applications
JF - Topology and its Applications
IS - 2
ER -