| Title:
|
Cardinalities of DCCC normal spaces with a rank 2-diagonal (English) |
| Author:
|
Xuan, Wei-Feng |
| Author:
|
Shi, Wei-Xue |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
457-461 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A topological space $X$ has a rank 2-diagonal if there exists a diagonal sequence on $X$ of rank $2$, that is, there is a countable family $\{\mathcal U_n\colon n\in \omega \}$ of open covers of $X$ such that for each $x \in X$, $\{x\}=\bigcap \{{\rm St}^2(x, \mathcal U_n)\colon n \in \omega \}$. We say that a space $X$ satisfies the Discrete Countable Chain Condition (DCCC for short) if every discrete family of nonempty open subsets of $X$ is countable. We mainly prove that if $X$ is a DCCC normal space with a rank 2-diagonal, then the cardinality of $X$ is at most $\mathfrak c$. Moreover, we prove that if $X$ is a first countable DCCC normal space and has a $G_\delta $-diagonal, then the cardinality of $X$ is at most $\mathfrak c$. (English) |
| Keyword:
|
cardinality |
| Keyword:
|
Discrete Countable Chain Condition |
| Keyword:
|
normal space |
| Keyword:
|
rank 2-diagonal |
| Keyword:
|
$G_\delta $-diagonal |
| MSC:
|
54D20 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 06674855 |
| idMR:
|
MR3576792 |
| DOI:
|
10.21136/MB.2016.0027-15 |
| . |
| Date available:
|
2017-01-03T15:13:44Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145960 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
