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A Non-Hausdorff Multifunction Ascoli Theorem for 𝓴3-Spaces

Published online by Cambridge University Press:  20 November 2018

Pedro Morales
Pedro Morales*
Affiliation:
Université de Montréal, Montréal, Québec
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A non-Hausdorff Ascoli theorem for continuous functions was established in [6]. The present purpose is to extend this result to point-compact continuous multifunction, using Levine's generalization for closed subsets [12]. The paper is organized as follows: the object of section 2 is to establish the necessary multifunction lemmas and to introduce the notion of a Tychonoff set; section 3 generalizes to multifunction context the partial exponential law of R. H. Fox [9, p. 430], and establishes a special exponential law for multifunctions; section 4 concerns the crucial properties of even continuity for multifunctions, introduced in [8]; the main theorem of the paper is established in section 5.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 893 - 900
Copyright
Copyright © Canadian Mathematical Society 1975

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