A characterizaton of R² by the concept of mild convexity

Sjur Flam

Vol. 79 (1978), No. 2, 371–373

DOI: 10.2140/pjm.1978.79.371

Abstract

Let S be an open, connected set in a locally convex, Hausdorff topological vector space L. If the boundary of S contains exactly one point not a mild convexity point of S and this point is not isolated in bd S, then dimL = 2.

Mathematical Subject Classification 2000

Primary: 52A05

Milestones

Received: 24 January 1978

Revised: 18 April 1978

Published: 1 December 1978