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Weak Families of Maps

Published online by Cambridge University Press:  20 November 2018

J. C. Taylor
J. C. Taylor*
Affiliation:
McGill University
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Let Ω be an index set and for each αϵΩ let fα:X → Xα be a function where X and Xα are sets. Assume that, for each α, a topology is given for Xα. Then, as is well-known, the functions fα and the topologies determine a topology for X. This is the so-called weak or initial topology, which is generated by .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 771 - 781
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bourbaki, N., Topologie Générale, Actualités Sci. Ind. 1142 3éme éd., 1961.Google Scholar
2. Bourbaki, N., Théorie des Ensembles, Actualités Sci. Ind. 1258, 1957.Google Scholar
3. Ehresmann, D., Structures Quotient, Comm. Math. Helvetici, vol.38 (1964), 219-242.Google Scholar
4. Gillman, L. and Jerison, M., Rings of Continuous Functions, New York, 1960.Google Scholar
5. Kelley, J. L., General Topology, New York, 1955.Google Scholar