Advanced Search

For a subset $A$ of the real line $ℝ$, Hattori space $H\left(A\right)$ is a topological space whose underlying point set is the reals $ℝ$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H\left(A\right)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in...