Last-modified: 2010-11-27 (土) 17:18:38
A Hausdorff space X is called equi-locally convex (ELCX) if there exists an open neighborhood U of the diagonal , a mapping and an open cover of X such that:
- for any t in I and x in X, ;
- for any x,y in X, and ;
- for any , ;
- for any , .
A subset W in X is called convex if and .
The cover is called a convex open cover of X.
An ELCX space is called coparacompact if any open cover has a locally finite convex refinement.
Vladimir P. Okhezin, On the fixed-point theory for non-compact maps and spaces.I, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center, Volume 5, 1995, 83-100.