A Note on the Fixed Point Property of Non-metric Tree-Like Continua - Lončar, Ivan (Sarajevo Journal of Mathematics, 2024)
The main purpose of this paper is to study the fixed point property of non-metric tree-like continua. It is proved, using the inverse systems method, that if $X$ is a non-metric tree-like continuum and if $h:X→ X$ is a periodic homeomorphism, then $h$ has the fixed point property (Theorem 2.4). Some theorems concerning the fixed point property of arc-like non-metric continua are also given. 2000 Mathematics Subject Classification. Primary 54H25, 54F15; Secondary 54B35