On the topology of locally 2-connected Peano continua

Abstract

Several recent results by Thomassen ([23 The locally connected compatc metric spaces embeddable in the plane, Combinatorica 24 (2004), 699-718, 24] Classification of locally 2-connected compact metric spaces, Combinatorica 25 (2005), 85-103) concerning locally (2-)connected, compact, connected metrizable spaces are considered in the setting of continuum theory. By doing that we find out that Thomassen's theorems are closely related to classical powerful theorems, due to Kuratowski, Claytor and Borsuk, among others, which allow an alternative approach to them. This way we are able to generalize Thomassen's results to locally compact spaces.