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A CHARACTERIZATION OF CONVEXITY-PRESERVING MAPS FROM A SUBSET OF A VECTOR SPACE INTO ANOTHER VECTOR SPACE

Published online by Cambridge University Press:  24 August 2001

K. A. ARIYAWANSA ,
W. C. DAVIDON  and
K. D. McKENNON
K. A. ARIYAWANSA
Affiliation:
Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164-3113, USA; ari@wsu.edu
W. C. DAVIDON
Affiliation:
Department of Mathematics, Haverford College, Haverford, PA 19041, USA; wdavidon@haverford.edu
K. D. McKENNON
Affiliation:
775 SE Edge Knoll Drive, Pullman, WA 99163, USA; zhisheng@turbonet.com
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Abstract

Let V and X be Hausdorff, locally convex, real, topological vector spaces with dim V > 1. It is shown that a map σ from an open, connected subset of V onto an open subset of X is homeomorphic and convexity-preserving if and only if σ is projective.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 179 - 190
Copyright
The London Mathematical Society 2001

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