| Title:
|
Components and inductive dimensions of compact spaces (English) |
| Author:
|
Krzempek, Jerzy |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
445-456 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that for every pair of natural numbers $m\geq n\geq 1$, there exists a compact Fréchet space $X_{m,n}$ such that \item {(a)} $\mathop{\rm dim}X_{m,n}=n$, $\mathop{\rm ind}X_{m,n}=\mathop{\rm Ind}X_{m,n}=m$, and \item {(b)} every component of $X_{m,n}$ is homeomorphic to the $n$-dimensional cube $I^n$. \endgraf \noindent This yields new counter-examples to the theorem on dimension-lowering maps in the cases of inductive dimensions. (English) |
| Keyword:
|
inductive dimension |
| Keyword:
|
theorem on dimension-lowering maps |
| Keyword:
|
component. |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 1224.54077 |
| idMR:
|
MR2657961 |
| . |
| Date available:
|
2010-07-20T16:51:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140581 |
| . |
| 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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