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A multifunction generalization of Gale's Ascoli theorem

Published online by Cambridge University Press:  09 April 2009

Geoffrey Fox  and
Pedro Morales
Geoffrey Fox
Affiliation:
Université de Montréal Montréal, Québec Canada
Pedro Morales
Affiliation:
Université de Montréal Montréal, Québec Canada
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Our purpose is to improve the Gale-type multifunction Ascoli theorem of Mancuso (1971; page 470). This latter supposes the range space to be normal and Hausdorff, and therefore does not contain Gale's theorem (1950; page 304). To obtain a multifunction theorem containing Gale's theorem (also Mancuso's theorem), we return to Gale's essential hypotheses. Thus, we assume the regularity of the range space in the sufficiency direction, and, in the necessity direction, weassume the domain to be a k-space and the range to be a regular Hausdorff space. We dispense with the “point-like” condition imposed by Mancuso. Unexplained terminology and notation is that of Mancusopos;s paper.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 2 , September 1975 , pp. 165 - 171
Copyright
Copyright © Australian Mathematical Society 1975

References

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