Remarks on almost Rothberger spaces and weakly Rothberger spaces

Abstract

A space X is almost Rothberger (weakly Rothberger) if for each sequence (u_n : n ∊ ℕ) of open covers of X there exists a sequence (U_n : n ∊ ℕ) such that for every n ∊ ℕ, U ∊ u_n and ∪_n∊ℕ = X (resp., = X). In this paper, we investigate the relationships among Rothberger spaces, almost Rothberger spaces and weakly Rothberger spaces, and also study topological properties of almost Rothberger spaces and weakly Rothberger spaces.