| Title:
|
An observation on spaces with a zeroset diagonal (English) |
| Author:
|
Xuan, Wei-Feng |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
15-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We say that a space $X$ has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of $X$ is countable. A space $X$ has a zeroset diagonal if there is a continuous mapping $f\colon X^2 \rightarrow [0,1]$ with $\Delta _X=f^{-1}(0)$, where $\Delta _X=\{(x,x)\colon x\in X\}$. In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most $\mathfrak c$. (English) |
| Keyword:
|
first countable |
| Keyword:
|
discrete countable chain condition |
| Keyword:
|
zeroset diagonal |
| Keyword:
|
cardinal |
| MSC:
|
54D20 |
| MSC:
|
54E35 |
| idZBL:
|
07217176 |
| idMR:
|
MR4088689 |
| DOI:
|
10.21136/MB.2018.0016-18 |
| . |
| Date available:
|
2020-03-12T08:17:58Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148060 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
