A note on monotone countable paracompactness

Abstract. We show that a space is MCP (monotone countable para-compact) if and only if it has property (∗), introduced by Teng, Xia and Lin. The relationship between MCP and stratifiability is highlighted by a similar characterization of stratifiability. Using this result, we prove that MCP is preserved by both countably biquotient closed and periph-erally countably compact closed mappings, from which it follows that both strongly Fréchet spaces and q-space closed images of MCP spaces are MCP. Some results on closed images of wN spaces are also noted. A space X is said to be monotonically countably metacompact (MCM) (see [1]) if there is an operator U assigning to each decreasing sequence (Dj)j∈ω of closed sets with empty intersection, a sequence of open sets U((Dj)) = U(n, (Dj)) n∈ω such that (1) Dn ⊆ U(n, (Dj)) for each n ∈ ω