Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T21:48:26.570Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

Information

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