## Tsukuba Journal of Mathematics

### Rays and the fixed point property in noncompact spaces

#### Abstract

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

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

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163163

Digital Object Identifier
doi:10.21099/tkbjm/1496163163

Mathematical Reviews number (MathSciNet)
MR1467223

Zentralblatt MATH identifier
0885.54026

#### Citation

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