Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-07T16:44:25.302Z Has data issue: false hasContentIssue false
  • English
  • Français

Projective bitopological spaces II.

Published online by Cambridge University Press:  09 April 2009

M. C. Datta
M. C. Datta
Affiliation:
Department of Mathematics, Birla Institute of Technology and SciencePilani (Rajasthan), India
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.

Gleason [3] proved that in the category G of compact Hausdorff spaces and continuous maps, the projective objects are precisely the extremally disconnected spaces contained in the category. Strauss [7] generalised this and proved that in the category G of regular Hausdorif spaces and perfect maps the projective objects are again precisely the extremally disconnected ones. Observe that Gleason's category is a full subcategory of Strauss's category.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 119 - 128
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Datta, M. C., ‘Projective bitopological spaces’, Journal of the Australian Math. Soc. 13 (1972), 327–334.CrossRefGoogle Scholar
[2]Fletcher, P., Hoyle, H. B. III and Patty, C. W., ‘The comparison of topologies’, Duke Math. Journ. 36 (1969), 325–332.CrossRefGoogle Scholar
[3]Gleason, A. M., ‘Projective topological spaces’, Jill. Journ. Math. 2 (1958), 482–489.Google Scholar
[4]Kelly, J. C., ‘Bitopological spaces’, Proc. Lond. Math. Soc., 3, 13 (1963), 71–89.CrossRefGoogle Scholar
[5]Moore, T. O., Elementary General Topology (Prentice-Hall, Englewood Cliffs, N. J., 1964).Google Scholar
[6]Pervin, W. J., ‘Connectedness in bitopological spaces’, Ind. Math. 29 (1967), 369–372.CrossRefGoogle Scholar
[7]Strauss, D. P., ‘Extremally disconnected spaces’, Proc. Amer. Math. Soc. 18 (1967) 305–309.CrossRefGoogle Scholar
[8]Thron, W. J., Topological Structures (Holt, Rinehart and Winston, New York, 1966).Google Scholar