“Image of a Hausdorff arc” is cyclically extensible and reducible

Abstract:

It is shown that a Hausdorff continuum $S$ is the continuous image of an arc (respectively arcwise connected) if and only if each cyclic element of $S$ is the continuous image of an arc (respectively, arcwise connected). Also, there is given an analogue to the metric space cyclic chain approximation theorem of G. T. Whyburn which applies to locally connected Hausdorff continua.