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The Homology of Uniform Spaces

Published online by Cambridge University Press:  20 November 2018

Mohammed Bahauddin  and
John Thomas
Mohammed Bahauddin
Affiliation:
St. Cloud State College, St. Cloud, Minnesota
John Thomas
Affiliation:
St. Cloud State College, St. Cloud, Minnesota
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In the past thirty years, algebraic topologists have developed a great body of knowledge concerning the category of topological spaces. By contrast, corresponding problems in the category of uniform spaces have been barely touched. Lubkin [8] studied the notion of a covering space in the category of generalized uniform spaces, and suggested that much of algebraic topology could be profitably studied in this category. Deming [2] discussed the fundamental group of a generalized uniform space, and related it to the first Čech homology group. A slightly different version of Cech cohomology was defined by Kuzminov and Svedov in [7] and related to the dimension theory of uniform spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 449 - 455
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Alfsen, E. M. and Fenstad, J. E., A note on completion and compactification, Math. Scand. 8 (1960), 105–115.Google Scholar
2. Deming, R. W., Some point-set properties and the edge path group of a generalized uniform space, Trans. Amer. Math. Soc. ISO (1968), 387-405.Google Scholar
3. Dowker, C. H., Homology groups of relations, Ann. of Math. 56 (1952), 84–95.Google Scholar
4. Dowker, C. H., Mapping theorems for non-compact spaces, Amer. J. Math. 69 (1947), 200–242.Google Scholar
5. Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton Univ. Press, Princeton, 1952).Google Scholar
6. Isbell, J. R., Uniform neighborhood retracts, Pacific J. Math. 11 (1961), 609–648.Google Scholar
7. Kuzminov, V. and Svedov, I., Cohomology and dimension of uniform spaces, Soviet Math. Dokl. 1 (1960), 1383–1386.Google Scholar
8. Lubkin, S., Theory of covering spaces, Trans. Amer. Math. Soc. 104 (1962), 265–278.Google Scholar
9. Simon, B., Some pictorial compactifications of the real line, Amer. Math. Monthly 76 (1964), 536–538.Google Scholar
10. Thron, W. J., Topological structures (Holt, Rinehart and Winston, New York, 1966).Google Scholar
11. Tukey, J. W., Convergence and uniformity in topology (Princeton Univ. Press, Princeton. 1940).Google Scholar