| Title:
|
Sequential completeness of subspaces of products of two cardinals (English) |
| Author:
|
Frič, Roman |
| Author:
|
Kemoto, Nobuyuki |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
119-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\kappa $ be a cardinal number with the usual order topology. We prove that all subspaces of $\kappa ^2$ are weakly sequentially complete and, as a corollary, all subspaces of $\omega _1^2$ are sequentially complete. Moreover we show that a subspace of $(\omega _1+1)^2$ need not be sequentially complete, but note that $X=A\times B$ is sequentially complete whenever $A$ and $B$ are subspaces of $\kappa $. (English) |
| Keyword:
|
sequentially continuous |
| Keyword:
|
sequentially complete |
| Keyword:
|
product space |
| MSC:
|
54A20 |
| MSC:
|
54B10 |
| MSC:
|
54C08 |
| idZBL:
|
Zbl 0949.54004 |
| idMR:
|
MR1676829 |
| . |
| Date available:
|
2009-09-24T10:20:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127472 |
| . |
| Reference:
|
[F1] R. Frič: Sequential envelope and subspaces of the Čech-Stone compactification.In General Topology and its Relations to Modern Analysis and Algebra III (Proc. Third Prague Topological Sympos., 1971), Academia, Praha, 1971, pp. 123–126. MR 0353260 |
| Reference:
|
[F2] R. Frič: On E-sequentially regular spaces.Czechoslovak Math. J. 26 (1976), 604–612. MR 0428240 |
| Reference:
|
[FK] R. Frič and V. Koutník: Sequentially complete spaces.Czechoslovak Math. J. 29 (1979), 287–297. MR 0529516 |
| Reference:
|
[Ki] J. Kim: Sequentially complete spaces.J. Korean Math. Soc. 9 (1972), 39–43. Zbl 0242.54024, MR 0303508 |
| Reference:
|
[Ko] V. Koutník: On sequentially regular convergence spaces.Czechoslovak Math. J. 17 (1967), 232–247. MR 0215277 |
| Reference:
|
[KOT] N. Kemoto, H. Ohta and K. Tamano: Products of spaces of ordinal numbers.Top. Appl. 45 (1992), 245–260. MR 1180812 |
| Reference:
|
[No] J. Novák: On sequential envelope.In General Topology and its Relations to Modern Analysis and Algebra I (Proc. First Prague Topological Sympos., 1961 ), Publishing House of the Czecoslovak Academy of Sciences, Praha, 1962, pp. 292–294. MR 0175082 |
| . |
