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Extensions of Closure Spaces

Published online by Cambridge University Press:  20 November 2018

K. C. Chattopadhyay  and
W. J. Thron
K. C. Chattopadhyay
Affiliation:
Panjab University, Chandigarh, India
W. J. Thron
Affiliation:
Panjab University, Chandigarh, India
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Extension theory has been intensively studied for completely regular spaces and is fairly well developed for T0-topological spaces. (See, for example, [1] and [5]). However, except for definitions of some of the basic concepts in [4] and results on embedding of closure spaces in cubes in [2] and [7], ours is the first study of the general theory of extensions of G0-closure spaces. (Definitions will be given following these introductory paragraphs).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1277 - 1286
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Banaschewski, B., Extensions of topological spaces, Can. Math. Bull. 7 (1964), 1–22.Google Scholar
2. Cech, E., Topological spaces, rev. ed. (Publ. House Czech. Acad. Sc. Prague, English transi. Wiley, New York, 1966).Google Scholar
3. Gagrat, M.S. and Naimpally, S. A., Proximity approach to extension problems, Fund. Math. 71 (1971), 63–76.Google Scholar
4. Gagrat, M. S. and Thron, W. J., Nearness structures and proximity extensions, Trans. Amer. Math. Soc. 208 (1975), 103–125.Google Scholar
5. Thron, W. J., Topological structures (Holt, Rinehart and Winston, New York, 1966).Google Scholar
6. Thron, W. J. Proximity structures and grills, Math. Ann. 206 (1973), 35–62.Google Scholar
7. Thron, W. J. and Warren, R. H., On the lattice of proximities of Cech compatible with a givenclosure space, Pac. J. Math. 49 (1973), 519–535.Google Scholar