THIN AND BOUNDED SUBSETS OF FREE TOPOLOGICAL-GROUPS

被引：6
|
作者：
SIPACHEVA, OV
TKACENKO, MG
机构：
[1] MV LOMONOSOV STATE UNIV,FAC MECH & MATH,CHAIR GEN TOPOL & GEOMET,MOSCOW 117234,USSR
[2] KALININ STATE UNIV,DEPT MATH,KALININ 170000,USSR
来源：
TOPOLOGY AND ITS APPLICATIONS | 1990年 / 36卷 / 02期
关键词：
bounded subset; free topological group; P-space; precompact subset; set support; thin subset; topological group;
D O I：
10.1016/0166-8641(90)90005-M
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that if B is a thin subset of a free topological group FM(X), then supp(B) is thin in FM(X) where supp(B) is the minimal set A ⊂ X with the property B ⊂ gp(A), and gp(A) is the group envelope of A. If X is not a P-space, then B ⊂ FM(X) is thin in FM(X) iff supp(B) is bounded in X. © 1990.
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页码：143 / 156
页数：14
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