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Nearly Open, According to a Subset, Linear Maps Which are Open

Published online by Cambridge University Press:  20 November 2018

J. Ch. Pomerol
J. Ch. Pomerol*
Affiliation:
Laboratoire d'Econométrie de l'UniversitéP. et M. Curie 4 Place Jussieu, 75230 Paris Cedex 5, France
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Abstract

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For a linear map we introduce two notions of being open according to a subset. With these two definitions, we characterize the linear, nearly open mappings which are open. Thus we generalize a famous theorem of V. Pták.

Keywords

46A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 96 - 101
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. De Wilde, M., Closed graph theorems and webbed spaces, Research notes in mathematics 19, Pitman, London, 1978.Google Scholar
2. Mennicken, R. and Sagraloff, B., Characterizations of nearly-openness, J. Reine Angew. Math. 313, 105–115, 1980.Google Scholar
3. Pomerol, J-Ch., Is the image of a closed convex set by a continuous linear mapping, closed?, Operations Research Verfahren 28, 412-419, 1978.Google Scholar
4. Pomerol, J-Ch.,Contribution à la programmation mathématiaue: existence de multiplicateurs de Lagrange et stabilité, Thèse de l'université P. et M. Curie, multigraphié, Paris, 1980.Google Scholar
5. Pták, V., Completness and the open mapping theorem, Bull. Soc. Math. France 86, 41-74, 1958.Google Scholar
6. Schaefer, H. H., Topological vector spaces, Graduate texts in mathematics 3, Springer, New York, 1971.Google Scholar