Selection topologies

Each weak selection for a space X defines an order-like relation, which in turn defines an open interval-like topology on X, called a selection topology. Spaces whose topology is determined by a collection of such selection topologies are called weak selection spaces. In this paper, we show that in the realm of second countable spaces, these are precisely the suborderable spaces. Motivated by this result, we refine an earlier result for weak orderability of second countable spaces.