Tsukuba Journal of Mathematics

Rays and the fixed point property in noncompact spaces

Tadeusz Dobrowolski and Witold Marciszewski

Full-text: Open access


We are concerned with the question of whether a noncompact space with a nice local structure contains a ray, i.e., a closed homeomorph of $[0,1)$. We construct rays in incomplete locally path connected spaces, and also, in noncompact metrizable convex sets; as a consequence these spaces lack the fixed point property. On the other hand, we give an example of a noncompact (nonmetrizable) convex subset $C$ of a locally convex topological vector space $E$ which has the fixed point property.

Article information

Tsukuba J. Math., Volume 21, Number 1 (1997), 97-112.

First available in Project Euclid: 30 May 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Dobrowolski, Tadeusz; Marciszewski, Witold. Rays and the fixed point property in noncompact spaces. Tsukuba J. Math. 21 (1997), no. 1, 97--112. doi:10.21099/tkbjm/1496163163. https://projecteuclid.org/euclid.tkbjm/1496163163

Export citation