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Journal of the London Mathematical Society 2001 64(1):179-190; doi:10.1017/S0024610701002204
© 2001 by London Mathematical Society
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© The London Mathematical Society

A Characterization of Convexity-Preserving Maps from a Subset of a Vector Space into Another Vector Space

K. A. Ariyawansa, W. C. Davidon and K. D. McKennon

Department of Pure and Applied Mathematics, Washington State University Pullman, WA 99164-3113, USA, ari{at}wsu.edu
Department of Mathematics, Haverford College Haverford, PA 19041, USA, wdavidon{at}haverford.edu
775 SE Edge Knoll Drive, Pullman, WA 99163, USA, zhisheng{at}turbonet.com

Received 12 January 2000. Revision received 23 November 2000.

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


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