| Title:
|
Functions that map cozerosets to cozerosets (English) |
| Author:
|
Larson, Suzanne |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
507-521 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A function $f$ mapping the topological space $X$ to the space $Y$ is called a {\it z-open\/} function if for every cozeroset neighborhood $H$ of a zeroset $Z$ in $X$, the image $f(H)$ is a neighborhood of $\operatorname{cl}_Y(f(Z))$ in $Y$. We say $f$ has the {\it z-separation property\/} if whenever $U$, $V$ are cozerosets and $Z$ is a zeroset of $X$ such that $U\subseteq Z\subseteq V$, there is a zeroset $Z'$ of $Y$ such that $f(U)\subseteq Z'\subseteq f(V)$. A surjective function is z-open if and only if it maps cozerosets to cozerosets and has the z-separation property. We investigate z-open functions and other functions that map cozerosets to cozerosets. We show that if $f$ is a continuous z-open function, then the Stone extension of $f$ is an open function. This is used to show several properties of topological spaces related to F-spaces are preserved under continuous z-open functions. (English) |
| Keyword:
|
open function |
| Keyword:
|
cozeroset preserving function |
| Keyword:
|
z-open function |
| Keyword:
|
F-space |
| Keyword:
|
SV space |
| Keyword:
|
finite rank |
| MSC:
|
54C10 |
| MSC:
|
54C30 |
| MSC:
|
54C45 |
| MSC:
|
54G05 |
| idZBL:
|
Zbl 1199.54099 |
| idMR:
|
MR2374130 |
| . |
| Date available:
|
2009-05-05T17:04:21Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119675 |
| . |
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| . |
