کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516987 | 1633128 | 2005 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The natural mappings in and k-subspaces of free topological groups on metrizable spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The natural mappings in and k-subspaces of free topological groups on metrizable spaces The natural mappings in and k-subspaces of free topological groups on metrizable spaces](/preview/png/9516987.png)
چکیده انگلیسی
Let F(X) be the free topological group on a Tychonoff space X. For all natural number n we denote by Fn(X) the subset of F(X) consisting of all words of reduced length ⩽n, and by in the natural mapping from (XâXâ1â{e})n to Fn(X). We prove that for a metrizable space X if Fn(X) is a k-space for each n, then X is locally compact and either separable or discrete. Therefore, as a corollary, we obtain that for a metrizable space X if Fn(X) is a k-space for all nâN, then so is F(X). Furthermore, it is proved that for a metrizable space X the following are equivalent: (i) the mapping in is a quotient mapping for each n; (ii) a subset U of F(X) is open if inâ1(Uâ©Fn(X)) is open in (XâXâ1â{e})n for each n; (iii) X is locally compact separable or discrete.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volumes 146â147, 1 January 2005, Pages 239-251
Journal: Topology and its Applications - Volumes 146â147, 1 January 2005, Pages 239-251
نویسندگان
Kohzo Yamada,