This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a nondegenerate chainable continuum. This paper is concerned with conditions under which a metric continuum (a compact connected metric space) contains a non-degenerate chainable continuum. By R.H. Bing’s theorem eleven [2] if a metric continuum X contains a non-degenerate subconti...

Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of X is no greater than c, the cardinality of the continuum. We go on to...