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Projective bitopological spaces

Published online by Cambridge University Press:  09 April 2009

M. C. Datta
M. C. Datta
Affiliation:
Department of Mathematics Birla Institute of Technology and Science Pilani (Rajasthan), India
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J. C. Kelly [2] introduced the concept of a bitopological space. Lane [3], Patty [4] and Pervin [5] have continued his work. Our purpose in this paper is to identify the projective objects in a suitable category of bitopological spaces after the manner of Gleason [1] and generalize his theorem that in the category of compact Hausdoriff topological spaces, the projective spaces are precisely the extremally disconnected ones.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 327 - 334
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Gleason, A. M., ‘Projective topological spaces’, Illi. J. Math. 2 (1958), 482–489.Google Scholar
[2]Kelly, J. C., ‘Bitopological spaces’, Proc. Lond. Math. Soc. (3) 13 (1963), 71–89.CrossRefGoogle Scholar
[3]Lane, E. P., ‘Bitopological spaces and quasi-uniform spaces’, Proc. Lond. Math. Soc. (3) 17 (1967), 241–256.CrossRefGoogle Scholar
[4]Patty, C. W., ‘Bitopological spaces’, Duke Math. Journ. 34 (1967), 387–391.CrossRefGoogle Scholar
[5]Pervin, W. J., ‘Connectedness in bitopological spaces’, Ind. Math. 29 (1967), 369–372.CrossRefGoogle Scholar