| Title:
|
Some non-multiplicative properties are $l$-invariant (English) |
| Author:
|
Tkachuk, Vladimir V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
169-175 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A cardinal function $\varphi$ (or a property $\Cal P$) is called $l$-invariant if for any Tychonoff spaces $X$ and $Y$ with $C_p(X)$ and $C_p(Y)$ linearly homeomorphic we have $\varphi(X)=\varphi(Y)$ (or the space $X$ has $\Cal P$ ($\equiv X\vdash {\Cal P}$) iff $Y\vdash\Cal P$). We prove that the hereditary Lindelöf number is $l$-invariant as well as that there are models of $ZFC$ in which hereditary separability is $l$-invariant. (English) |
| Keyword:
|
$l$-equivalent spaces |
| Keyword:
|
$l$-invariant property |
| Keyword:
|
hereditary Lindelöf number |
| MSC:
|
54A25 |
| MSC:
|
54A35 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 0886.54005 |
| idMR:
|
MR1455481 |
| . |
| Date available:
|
2009-01-08T18:29:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118913 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: Structure and classification of topological spaces and cardinal invariants (in Russian).Uspehi Mat. Nauk 33 6 (1978), 29-84. MR 0526012 |
| Reference:
|
[2] Arhangel'skii A.V.: On relationship between the invariants of topological groups and their subspaces (in Russian).Uspehi Mat. Nauk 35 3 (1980), 3-22. MR 0580615 |
| Reference:
|
[3] Arhangel'skii A.V.: Topological function spaces (in Russian).Moscow University Publishing House, Moscow, 1989. MR 1017630 |
| Reference:
|
[4] Arhangel'skii A.V.: $C_p$-theory.in: Recent Progress in General Topology, edited by J. van Mill and M. Hušek, North Holland, 1992, pp.1-56. Zbl 0932.54015, MR 1229121 |
| Reference:
|
[5] Arhangel'skii A.V., Ponomarev V.I.: General Topology in Problems and Exercises (in Russian).Nauka Publishing House, Moscow, 1974. MR 0239550 |
| Reference:
|
[6] Engelking R.: General Topology.PWN, Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[7] Gul'ko S.P., Khmyleva T.E.: The compactness is not preserved by $t$-equivalence (in Russian).Mat. Zametki 39 6 (1986), 895-903. MR 0855937 |
| Reference:
|
[8] Pestov V.G.: Some topological properties are preserved by $M$-equivalence (in Russian).Uspehi Mat. Nauk 39 6 (1984), 203-204. MR 0771108 |
| Reference:
|
[9] Tkachuk V.V.: On a method of constructing examples of $M$-equivalent spaces (in Russian).Uspehi Mat. Nauk 38 6 (1983), 127-128. MR 0728737 |
| Reference:
|
[10] Todorčević S.: Forcing positive partition relations.Trans. Amer. Math. Soc. 280 2 (1983), 703-720. MR 0716846 |
| . |
