Some remarks on $b$-paracompact spaces

A condition is found which is satisfied by a perfect normal image of a $b$-paracompact space. It is proved that a connected locally connected $b$-paracompact space, each of whose points has a fundamental system of neighborhoods with boundaries satisfying the Souslin condition, is Lindelöf. An example is constructed of a locally compact $b$-paracompact Hausdorff space having an open covering which cannot be refined by an open covering not containing infinitely many antidisjunctive families. The questions are considered of the imbedding of weakly paracompact and $b$-paracompact spaces in certain of their compactifications.