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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Additional Information

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