Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T04:48:17.123Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on [a, b]-Compact Spaces

Published online by Cambridge University Press:  20 November 2018

C. M. Pareek  and
H. Z. Hdeib
C. M. Pareek
Affiliation:
Mathematics Department Kuwait UniversityP.O. Box 5969 Kuwait
H. Z. Hdeib
Affiliation:
Mathematics Department Kuwait UniversityP.O. Box 5969 Kuwait
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we present an array of results which deals with the question "When is the product of two [a, b]-compact spaces an [a, b]-compact space".

In section 1, we give some essential terminology. In section 2, we define some new classes of functions and then obtain some product theorems. In section 3, we give some applications of the product theorems obtained in section 2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 1 , 01 March 1979 , pp. 105 - 112
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Bagley, R. W., Connell, F. H. and Mcknight, J. D. Jr., On properties characterizing pseudocompact spaces, Proc. Amer. Math. Soc, 9 (1958), 500-506.Google Scholar
2. Banerjee, R. N., Closed maps and countably metacompact spaces, J. Lond. Math. Soc, 8 (1974), 49-50.Google Scholar
3. Dieudonné, J., Une généralisation des espaces compacts, J. Math. Pures Appl., 23 (1944), 65-76.Google Scholar
4. Dowker, C. H., On countably paracompact spaces, Can. J. Math., 3 (1951), 219-224.Google Scholar
5. Gál, I. S., On a generalized notion of compactness I, Proc. Koninki. Nederl. Akad. Wetensch., 60 (1957), 421-435.Google Scholar
6. Halfer, E., Compact mappings, Proc. Amer. Math. Soc, 8 (1957), 828-830.Google Scholar
7. Hanai, S., Inverse images of closed mappings I, Proc. Japan Acad. 37 (1961), 298-301 Google Scholar
8. Hanai, S., On dosed mappings II, Proc. Japan Acad., 32 (1956), 388-391.Google Scholar
9. Hayashi, Y., On countably metacompact spaces, Bull. Univ. Osaka. Pref. Ser., A8 (1959/60), 161-164.Google Scholar
10. Henriksen, M. and Isbell, J. R., Some properties of compactifications, Duke Math. J., 25 (1958), 83-105.Google Scholar
11. Krajewski, L. L., On expanding locally finite collection, Can. J. Math., 23 (1971), 58-68.Google Scholar
12. Mansfield, M. J., Some generalizations of full normality, Tran. Amer. Math. Soc, 86 (1957), 489-505.Google Scholar
13. Michael, E., A note on paracompact spaces, Proc. Amer. Math. Soc, 8 (1957), 822-828.Google Scholar
14. Morita, K., Paracompactness and product spaces, Fund. Math., 50 (1961/62), 223-236.Google Scholar
15. Mrówka, S., Compactness and products spaces, Coll. Math., 7 (1959), 19-22.Google Scholar
16. Nardzewski, C., A remark on the cartesian product of compact spaces, Bull. Acad. Polon. Sci., 6 (1954), 265-266.Google Scholar
17. Nóvak, J., On the cartesian product of two compact spaces, Fund. Math., 40 (1953), 106-112.Google Scholar
18. Saks, V. and Stephenson, R. M., Products of m-compact spaces, Proc. Amer. Math. Soc, 28 (1971), 279-288.Google Scholar
19. Smith, J. C. and Krajewski, L. L., Expandability and collectionmse normality, Trans, Amer. Math. Soc, 160 (1971), 437-451.Google Scholar
20. Scarborough, C. T., Closed graph and closed projections, Proc. Amer. Math. Soc, 20 (1969), 465-470.Google Scholar