| Title:
|
Strongly sequential spaces (English) |
| Author:
|
Mynard, Frédéric |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
143-153 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces. (English) |
| Keyword:
|
sequential |
| Keyword:
|
Fréchet |
| Keyword:
|
strongly Fréchet topology |
| Keyword:
|
product convergence |
| Keyword:
|
Antoine convergence |
| Keyword:
|
continuous convergence |
| MSC:
|
54A20 |
| MSC:
|
54B10 |
| MSC:
|
54B30 |
| MSC:
|
54D55 |
| idZBL:
|
Zbl 1090.54006 |
| idMR:
|
MR1756935 |
| . |
| Date available:
|
2009-01-08T18:59:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119149 |
| . |
| Reference:
|
[1] Bourdaud G.: Espaces d'Antoine et semi-espaces d'Antoine.Cahiers de Topologies et Géométrie Différentielle 16 107-133 (1975). Zbl 0315.54005, MR 0394529 |
| Reference:
|
[2] Choquet G.: Convergences.Ann. Inst. Fourier 23 55-112 (1947). MR 0025716 |
| Reference:
|
[3] Dolecki S.: Convergence-theoretic approach to quotient quest.Topology Appl. 73 1-21 (1996). Zbl 0862.54001, MR 1413721 |
| Reference:
|
[4] Dolecki S., Mynard F.: Convergence theoretic mechanisms behind product theorems.to appear in Topology Appl. Zbl 0953.54002, MR 1780899 |
| Reference:
|
[5] Engelking R.: Topology.PWN, 1977. Zbl 0932.01059 |
| Reference:
|
[6] Michael E.: A quintuple quotient quest.Gen. Topology Appl. 2 91-138 (1972). Zbl 0238.54009, MR 0309045 |
| Reference:
|
[7] Michael E.: Local compactness and cartesian product of quotient maps and $k$-spaces.Ann. Inst. Fourier (Grenoble) 19 281-286 (1968). MR 0244943 |
| Reference:
|
[8] Mynard F.: Coreflectively modified continuous duality applied to classical product theorems.to appear. Zbl 1007.54008, MR 1890032 |
| Reference:
|
[9] Olson R.C.: Biquotient maps, countably bisequential spaces and related topics.Topology Appl. 4 1-28 (1974). MR 0365463 |
| Reference:
|
[10] Tanaka Y.: Products of sequential spaces.Proc. Amer. Math. Soc. 54 371-375 (1976). Zbl 0292.54025, MR 0397665 |
| Reference:
|
[11] Tanaka Y.: Necessary and sufficient conditions for products of $k$-spaces.Topology Proc. 14 281-312 (1989). Zbl 0727.54012, MR 1107729 |
| . |
