Remarks on almost Rothberger spaces and weakly Rothberger spaces.

A spaceXisalmost Rothberger (weakly Rothberger)if for each sequence (un:n∊ ℕ) of open covers ofXthere exists a sequence (Un:n∊ ℕ) such that for every n ∊ ℕ,U∊unand ∪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. [ABSTRACT FROM PUBLISHER]