| Title:
|
Countable fan-tightness versus countable tightness (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Bella, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
565-576 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Countable tightness is compared to the stronger notion of countable fan-tight\-ness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation. (English) |
| Keyword:
|
tightness |
| Keyword:
|
fan-tightness |
| Keyword:
|
countably compact spaces |
| Keyword:
|
pseudo-compact space |
| Keyword:
|
P-point |
| Keyword:
|
biquotient mapping |
| MSC:
|
54A20 |
| MSC:
|
54A25 |
| MSC:
|
54C10 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 0881.54005 |
| idMR:
|
MR1426921 |
| . |
| Date available:
|
2009-01-08T18:26:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118863 |
| . |
| Reference:
|
[1] Arens R.: Note on convergence in topology.Math. Mag. 23 (1950), 229-234. Zbl 0041.31502, MR 0037500 |
| Reference:
|
[2] Arhangel'skii A.V.: Mappings and spaces.Russian Math. Surveys 21 (1966), 115-162. MR 0227950 |
| Reference:
|
[3] Arhangel'skii A.V.: Hurewicz spaces, analytic sets and fan-tightness of spaces of functions.Soviet Math. Dokl. 33 \number 2 (1986), 396-399. |
| Reference:
|
[4] Arhangel'skii A.V.: The frequency spectrum of a topological space and the product operation.Trans. Moscow Math. Soc. 40 (1981), 163-200. |
| Reference:
|
[5] Gruenhage G., Tanaka Y.: Products of $k$-spaces and spaces of countable tightness.Trans. Amer. Math. Soc. 273 \number 1 (1982), 299-308. Zbl 0491.54019, MR 0664043 |
| Reference:
|
[6] Harley P.W. III, Stephenson R.M., Jr.: Symmetrizable and related spaces.Trans. Amer. Math. Soc. 219 (1976), 89-111. MR 0418048 |
| Reference:
|
[7] Kannan V.: Every compact $T_5$ sequential space is Fréchet.Fund. Math. 107 (1980), 85-90. Zbl 0452.54019, MR 0584661 |
| Reference:
|
[8] Malykhin V.I.: On countable spaces having no bicompactification of countable tightness.Soviet Math. Dokl. 13 \number 5 (1972), 1407-1411. |
| Reference:
|
[9] Malykhin V.I.: An example of a topological group.in Topological spaces and their mappings, Riga. Latv. Gosud. Univ. (in Russian), 1981, pp. 120-123. Zbl 0478.22001, MR 0630428 |
| Reference:
|
[10] Michael E.A.: A quintuple quotient quest.Gen. Top. Appl. 2 (1972), 91-138. Zbl 0238.54009, MR 0309045 |
| Reference:
|
[11] Nedev S.: Symmetrizable spaces and final compactness.Soviet Math. Dokl. 8 (1967), 890-892. Zbl 0153.52701, MR 0216460 |
| Reference:
|
[12] Nyikos P.J.: Metrizability and the Fréchet-Urysohn property in topological groups.Proc. Amer. Math. Soc. 83 (1981), 793-801. Zbl 0474.22001, MR 0630057 |
| Reference:
|
[13] Siwiec F.: Sequence-covering and countably biquotient mappings.Gen. Top. Appl. 1 (1971), 143-154. MR 0288737 |
| Reference:
|
[14] Siwiec F.: Generalizations of the first axiom of countability.Rocky Mount. J. Math. 5 (1975), 1-60. Zbl 0294.54021, MR 0358699 |
| Reference:
|
[15] Siwiec F., Mancuso V.J.: Relations among certain mappings and conditions for their equivalence.Gen. Top. Appl. 1 (1971), 34-41. Zbl 0216.44203, MR 0282347 |
| Reference:
|
[16] Stephenson M., Jr: Symmetrizable, ${\Cal F}$-, and weakly first countable spaces.Can. J. Math. XXIX (1977), 480-488. MR 0442885 |
| Reference:
|
[17] Tamano K.: Closed images of metric spaces and metrization.Topology Proceedings 10 (1985), 177-186. Zbl 0616.54026, MR 0851211 |
| Reference:
|
[18] Tanaka Y.: Product of spaces of countable tightness.Topology Proceedings 6 (1981), 115-133. MR 0650484 |
| Reference:
|
[19] Tanaka Y.: Metrizability of certain quotient spaces.Fund. Math. 119 (1983), 157-168. MR 0731817 |
| Reference:
|
[20] Todorcevic S.: Some applications of S and L combinatorics.Annals New York Academy of Science, 1991, pp. 130-167. Zbl 0836.54018, MR 1277886 |
| Reference:
|
[21] Uspenskii V.V.: Frequency spectrum of functional spaces.Vestnik Mosk. Universiteta, Ser. Matematica 37\number 1 (1982), 31-35. |
| . |
