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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On infinite-dimensional features of proper and closed mappings


Author: R. S. Sadyrkhanov
Journal: Proc. Amer. Math. Soc. 98 (1986), 643-648
MSC: Primary 58C15
DOI: https://doi.org/10.1090/S0002-9939-1986-0861768-6
MathSciNet review: 861768
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Abstract: 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.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0861768-6
Keywords: Closed and proper maps, infinite-dimensional Fréchet manifolds
Article copyright: © Copyright 1986 American Mathematical Society