Countable fan-tightness versus countable tightness

Aleksander V. Arhangel'skii; Angelo Bella

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 565-576
  • ISSN: 0010-2628

Abstract

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Countable tightness is compared to the stronger notion of countable fan-tightness. 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.

How to cite

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Arhangel'skii, Aleksander V., and Bella, Angelo. "Countable fan-tightness versus countable tightness." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 565-576. <http://eudml.org/doc/247927>.

@article{Arhangelskii1996,
abstract = {Countable tightness is compared to the stronger notion of countable fan-tightness. 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.},
author = {Arhangel'skii, Aleksander V., Bella, Angelo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {tightness; fan-tightness; countably compact spaces; pseudo-compact space; P-point; biquotient mapping; tightness; fan-tightness; countably compact space; pseudo-compact space; P-point; biquotient mapping},
language = {eng},
number = {3},
pages = {565-576},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Countable fan-tightness versus countable tightness},
url = {http://eudml.org/doc/247927},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Arhangel'skii, Aleksander V.
AU - Bella, Angelo
TI - Countable fan-tightness versus countable tightness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 565
EP - 576
AB - Countable tightness is compared to the stronger notion of countable fan-tightness. 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.
LA - eng
KW - tightness; fan-tightness; countably compact spaces; pseudo-compact space; P-point; biquotient mapping; tightness; fan-tightness; countably compact space; pseudo-compact space; P-point; biquotient mapping
UR - http://eudml.org/doc/247927
ER -

References

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  1. Arens R., Note on convergence in topology, Math. Mag. 23 (1950), 229-234. (1950) Zbl0041.31502MR0037500
  2. Arhangel'skii A.V., Mappings and spaces, Russian Math. Surveys 21 (1966), 115-162. (1966) MR0227950
  3. Arhangel'skii A.V., Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Math. Dokl. 33 2(1986), 396-399. (1986) 
  4. Arhangel'skii A.V., The frequency spectrum of a topological space and the product operation, Trans. Moscow Math. Soc. 40 (1981), 163-200. (1981) 
  5. Gruenhage G., Tanaka Y., Products of k -spaces and spaces of countable tightness, Trans. Amer. Math. Soc. 273 1(1982), 299-308. (1982) Zbl0491.54019MR0664043
  6. Harley P.W. III, Stephenson R.M., Jr., Symmetrizable and related spaces, Trans. Amer. Math. Soc. 219 (1976), 89-111. (1976) MR0418048
  7. Kannan V., Every compact T 5 sequential space is Fréchet, Fund. Math. 107 (1980), 85-90. (1980) Zbl0452.54019MR0584661
  8. Malykhin V.I., On countable spaces having no bicompactification of countable tightness, Soviet Math. Dokl. 13 5(1972), 1407-1411. (1972) 
  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. Zbl0478.22001MR0630428
  10. Michael E.A., A quintuple quotient quest, Gen. Top. Appl. 2 (1972), 91-138. (1972) Zbl0238.54009MR0309045
  11. Nedev S., Symmetrizable spaces and final compactness, Soviet Math. Dokl. 8 (1967), 890-892. (1967) Zbl0153.52701MR0216460
  12. Nyikos P.J., Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), 793-801. (1981) Zbl0474.22001MR0630057
  13. Siwiec F., Sequence-covering and countably biquotient mappings, Gen. Top. Appl. 1 (1971), 143-154. (1971) MR0288737
  14. Siwiec F., Generalizations of the first axiom of countability, Rocky Mount. J. Math. 5 (1975), 1-60. (1975) Zbl0294.54021MR0358699
  15. Siwiec F., Mancuso V.J., Relations among certain mappings and conditions for their equivalence, Gen. Top. Appl. 1 (1971), 34-41. (1971) Zbl0216.44203MR0282347
  16. Stephenson M., Jr, Symmetrizable, ℱ -, and weakly first countable spaces, Can. J. Math. XXIX (1977), 480-488. (1977) MR0442885
  17. Tamano K., Closed images of metric spaces and metrization, Topology Proceedings 10 (1985), 177-186. (1985) Zbl0616.54026MR0851211
  18. Tanaka Y., Product of spaces of countable tightness, Topology Proceedings 6 (1981), 115-133. (1981) MR0650484
  19. Tanaka Y., Metrizability of certain quotient spaces, Fund. Math. 119 (1983), 157-168. (1983) MR0731817
  20. Todorcevic S., Some applications of S and L combinatorics, Annals New York Academy of Science, 1991, pp. 130-167. Zbl0836.54018MR1277886
  21. Uspenskii V.V., Frequency spectrum of functional spaces, Vestnik Mosk. Universiteta, Ser. Matematica 371(1982), 31-35. (1982) 

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