On spaces with point-countable k -systems

Iwao Yoshioka

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 4, page 749-765
  • ISSN: 0010-2628

Abstract

top
This paper deals with the behavior of M -spaces, countably bi-quasi- k -spaces and singly bi-quasi- k -spaces with point-countable k -systems. For example, we show that every M -space with a point-countable k -system is locally compact paracompact, and every separable singly bi-quasi- k -space with a point-countable k -system has a countable k -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable k -systems.

How to cite

top

Yoshioka, Iwao. "On spaces with point-countable $k$-systems." Commentationes Mathematicae Universitatis Carolinae 45.4 (2004): 749-765. <http://eudml.org/doc/249384>.

@article{Yoshioka2004,
abstract = {This paper deals with the behavior of $M$-spaces, countably bi-quasi-$k$-spaces and singly bi-quasi-$k$-spaces with point-countable $k$-systems. For example, we show that every $M$-space with a point-countable $k$-system is locally compact paracompact, and every separable singly bi-quasi-$k$-space with a point-countable $k$-system has a countable $k$-system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable $k$-systems.},
author = {Yoshioka, Iwao},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {countably-bi-quasi-$k$-space; point-countable $k$-system; local compactness; metrizability; countably-bi-quasi--space; point-countable -system; local compactness; metrizability},
language = {eng},
number = {4},
pages = {749-765},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On spaces with point-countable $k$-systems},
url = {http://eudml.org/doc/249384},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Yoshioka, Iwao
TI - On spaces with point-countable $k$-systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 4
SP - 749
EP - 765
AB - This paper deals with the behavior of $M$-spaces, countably bi-quasi-$k$-spaces and singly bi-quasi-$k$-spaces with point-countable $k$-systems. For example, we show that every $M$-space with a point-countable $k$-system is locally compact paracompact, and every separable singly bi-quasi-$k$-space with a point-countable $k$-system has a countable $k$-system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable $k$-systems.
LA - eng
KW - countably-bi-quasi-$k$-space; point-countable $k$-system; local compactness; metrizability; countably-bi-quasi--space; point-countable -system; local compactness; metrizability
UR - http://eudml.org/doc/249384
ER -

References

top
  1. Arhangel'skii A.V., Factor mappings of metric spaces, Soviet Math. Dokl. 5 (1965), 368-371. (1965) 
  2. Arhangel'skii A.V., On a class of spaces containing all metric spaces and all locally bicompact spaces, Amer. Math. Soc. Transl. 92 (1970), 1-39. (1970) 
  3. Burke D.K., On p-spaces and w Δ -spaces, Pacific J. Math. 35 (1972), 285-296. (1972) MR0278255
  4. Burke D.K., Covering properties, Chapter 9, in Handbook of Set Theoretic Topology; K. Kunen and J.E. Vaughan, Eds., North Holland, Amsterdam, 1984. Zbl0569.54022MR0776628
  5. Burke D.K., Michael E., On certain point-countable covers, Pacific J. Math. 64 (1976), 79-92. (1976) Zbl0341.54022MR0467687
  6. Ceder J.G., Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-125. (1961) Zbl0103.39101MR0131860
  7. Engelking R., General Topology, Polish Sci. Publ., Warszawa, 1977. Zbl0684.54001MR0500780
  8. Franklin S.P., Spaces in which sequences suffice II, Fund. Math. 61 (1967), 51-56. (1967) Zbl0168.43502MR0222832
  9. Gillman L., Jerison M., Rings of Continuous Functions, D. Van Nostrand, Princeton, N.J., 1960. Zbl0327.46040MR0116199
  10. Gruenhage G., Michael E., Tanaka Y., Spaces determined by point-countable covers, Pacific J. Math. 113 (1984), 303-332. (1984) Zbl0561.54016MR0749538
  11. Heath R.W., On open mappings and certain spaces satisfying the first countability axiom, Fund. Math. 57 (1965), 91-96. (1965) Zbl0134.41802MR0179763
  12. Li J., Lin S., k ø m e g a -spaces and Y. Tanaka’s question, Acta Math. Hungar. 100 (2003), 321-323. (2003) 
  13. Martin H.W., Remarks on the Nagata-Smirnov metrization theorem, Topology Proceedings of the Memphis State Univ. Conference, edited by S.P. Franklin and B.V. Smith Thomas, Lecture Note in Pure and Applied Math. 24, pp.217-224, Dekker, 1976. Zbl0353.54018MR0433401
  14. Michael E., ℵ 0 -spaces, J. Math. Mech. 15 (1966), 983-1002. (1966) MR0206907
  15. Michael E., A quintuple quotient quest, General Topology Appl. 2 (1972), 91-138. (1972) Zbl0238.54009MR0309045
  16. O'Mera P., On paracompactness in function spaces with the compact-open topology, Proc. Amer. Math. Soc. 29 (1971), 183-189. (1971) MR0276919
  17. Stone A.H., Metrizability of unions of spaces, Proc. Amer. Math. Soc. 10 (1959), 361-366. (1959) MR0105672
  18. Tanaka Y., On open finite-to-one maps, Bull. Tokyo Gakugei Univ. Ser. IV 25 (1973), 1-13. (1973) Zbl0355.54008MR0346730
  19. Tanaka Y., Some necessary conditions for products of k -spaces, Bull. Tokyo Gakugei Univ. Ser. IV 30 (1978), 1-16. (1978) Zbl0427.54016MR0512222
  20. Tanaka Y., Point-countable k -systems and products of k -spaces, Pacific J. Math. 101 (1982), 199-208. (1982) Zbl0498.54023MR0671852
  21. Tanaka Y., Metrizability of certain point-countable unions, Sci. Math. Jpn. 57 (2003), 201-206. (2003) Zbl1032.54017MR1959977
  22. Tanaka Y., Products of k -spaces, and questions, Comment. Math. Univ. Carolinae 44 (2003), 335-345. (2003) Zbl1100.54006MR2026168
  23. Tanaka Y., Zhoh Hao-xuan, Spaces determined by metric subsets, and their character, Questions Answers Gen. Topology 3 (1985/86), 145-160. (1985/86) MR0826985
  24. Yoshioka I., On the metrizability of γ -spaces and k s -spaces, Questions Answers Gen. Topology 19 (2001), 55-72. (2001) MR1815346

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.