کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658512 | 1633098 | 2015 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Topological groups with a bc-base
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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: Topological groups with a bc-base Topological groups with a bc-base](/preview/png/4658512.png)
چکیده انگلیسی
Approximately 10 years ago, Zambakhidze asked whether every non-zero-dimensional topological group with a bc-base is locally compact. Below we show that the small inductive dimension ind of any non-locally compact group with such a base doesn't exceed 1. We prove, however, that a σ-compact non-locally compact topological group with a bc -base is zero-dimensional. Two more results in this paper are worth mentioning: 1) if the free topological group F(X)F(X) of a Tychonoff space X has a bc -base, then ind(X)≤0ind(X)≤0, and 2) a topological group G has a bc-base if and only if G can be compactified by a zero-dimensional remainder.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 179, 1 January 2015, Pages 5–12
Journal: Topology and its Applications - Volume 179, 1 January 2015, Pages 5–12
نویسندگان
A.V. Arhangel'skii, J. van Mill,