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A General Tychonoff Theorem for Multifunction

Published online by Cambridge University Press:  20 November 2018

Geoffrey Fox  and
Pedro Morales
Geoffrey Fox
Affiliation:
Université de Montréal, Montréal, Québec
Pedro Morales
Affiliation:
Université de Montréal, Montréal, Québec
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Let {Xa}a∈A be a non-empty family of compact spaces and let F be a subset of the m-product P{Xa:a∈A}. The Tychonoff problem is the determination of the sets F which are pointwise compact. It is known that P{Xa: a ∈ A} is pointwise compact [5, p. 400]. Also the set F of all point-closed multifunctions of P{Xa:a∈ A) is pointwise compact.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 519 - 521
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Berge, C., Topological Spaces, The Macmillan Company, New York (1963).Google Scholar
2. Fox, G. and Morales, P., A Multifunction Generalization of Gale's Ascoli Theorem, to appear in J. Austral. Math. Soc.Google Scholar
3. Frink, O., Topology in Lattices, Trans. Amer. Math. Soc. 51 (1942), 569-582.Google Scholar
4. Kelley, J., General Topology, D. Van Nostrand, New York (1965).Google Scholar
5. Lin, Y. F., Tychonoff s Theorem for the Space of Multifunctions, Amer. Math. Monthly 74 (1967), 399-400.Google Scholar
6. Mancuso, V. J., An Ascoli Theorem for Multi-Valued Functions, J. Austral. Math. Soc. 12 (1971), 466-472.Google Scholar
7. Michael, E., Topologies on Spaces of Subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182.Google Scholar
8. Smithson, R. E., Topologies on Sets of Relations, J. Natur. Sci. and Math. (Lahore) 11 (1971), 43-50.Google Scholar
9. Smithson, R. E., Uniform Convergence for Multifunctions, Pacific J. Math. 39 (1971), 253-260.Google Scholar
10. Smithson, R. E., Multifunctions, Nieuw Arch. Wisk. 20 (1972), 31-53.Google Scholar
11. Strother, W., Multi-homotopy, Duke J. Math. 22 (1955), 281-285.Google Scholar