| Title:
|
Densely continuous forms, pointwise topology and cardinal functions (English) |
| Author:
|
Holý, Dušan |
| Author:
|
Vadovič, Peter |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
79-92 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the space $D(X,Y)$ of densely continuous forms introduced by Hammer and McCoy and investigated also by Holá . We show some additional properties of $D(X,Y)$ and investigate the subspace $D^*(X)$ of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence $\tau _p$. The largest part of the paper is devoted to the study of various cardinal functions for $(D^*(X),\tau _p)$, in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, $\pi $-weight, $\pi $-character, netweight etc. (English) |
| Keyword:
|
locally bounded densely continuous form |
| Keyword:
|
topology of pointwise convergence |
| Keyword:
|
cardinal function |
| Keyword:
|
weight |
| Keyword:
|
density |
| Keyword:
|
netweight |
| Keyword:
|
cellularity |
| MSC:
|
54A25 |
| MSC:
|
54C60 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 1174.54010 |
| idMR:
|
MR2402527 |
| . |
| Date available:
|
2009-09-24T11:53:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128247 |
| . |
| Reference:
|
[1] G. Beer: Topologies on Closed and Closed Convex Sets.Kluwer Academic Publishers, Dordrecht, 1993. Zbl 0792.54008, MR 1269778 |
| Reference:
|
[2] C. Berge: Topological Spaces.Oliver and Boyd, Edinburgh, 1963. Zbl 0114.38602 |
| Reference:
|
[3] J. P. R. Christensen: Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings.Proceedings of the American Mathematical Society 86 (1982), 649–655. MR 0674099, 10.1090/S0002-9939-1982-0674099-0 |
| Reference:
|
[4] R. Engelking: General Topology.PWN - Polish Scientific Publishers, Warsaw, 1977. Zbl 0373.54002, MR 0500780 |
| Reference:
|
[5] S. T. Hammer and R. A. McCoy: Spaces of densely continuous forms.Set-Valued Analysis 5 (1997), 247–266. MR 1486774, 10.1023/A:1008666504767 |
| Reference:
|
[6] ╝. Holá: Spaces of densely continuous forms, USCO and minimal USCO maps.Set-Valued Analysis 11 (2003), 133–151. MR 1966697, 10.1023/A:1022982924962 |
| Reference:
|
[7] ╝. Holá and R. A. McCoy: Cardinal invariants of the topology of uniform convergence on compact sets on the space of minimal USCO maps.Rocky Mountain Journal of Mathematics 37 (2007), 229–246. MR 2316446, 10.1216/rmjm/1181069328 |
| Reference:
|
[8] R. A. McCoy and I. Ntantu: Topological properties of spaces of continuous functions.Lecture Notes in Mathematics 1315, Springer-Verlag, Berlin, 1988. MR 0953314 |
| . |
