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On Infinite Dimensional Features of Proper and Closed Mappings
R. S. Sadyrkhanov
Proceedings of the American Mathematical Society
Vol. 98, No. 4 (Dec., 1986), pp. 643-648
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2045743
Page Count: 6
You can always find the topics here!Topics: Mathematical manifolds, Homeomorphism, Topological theorems, Topological spaces, Mathematical theorems, Respect, Countability
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We consider some global properties of continuous proper and closed maps acting in infinite-dimensional Fréchet manifolds. These essentially infinite-dimensional features are related to the following questions: 1. When is a closed map proper? 2. When can the "singularity set" of the map, i.e. the subset of the domain of definition where the map is not a local homeomorphism, be deleted? We establish the final answer to the first question and an answer to the second one when the singular set is a countable union of compact sets.
Proceedings of the American Mathematical Society © 1986 American Mathematical Society