View source for Strongly countably complete topological space

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A topological space $X$ for which there is a sequence $\{\mathcal A_i\}$ of open coverings of $X$ such that a sequence $\{F_i\}$ of closed subsets of $X$ has a non-empty intersection whenever $F_i\supset F_{i+1}$ for all $i$ and each $F_i$ is a subset of some member of $\mathcal A_i$.

Locally countably compact spaces and Čech-complete spaces are strongly countably complete. Every strongly countably complete space is a [[Baire space|Baire space]] (but not vice versa).

This rather technical notion plays an important role in questions whether separate continuity of a mapping on a product $X\times Y$ implies joint continuity on a large subset of $X\times Y$, see [[Namioka space|Namioka space]]; [[Namioka theorem|Namioka theorem]]; [[Separate and joint continuity|Separate and joint continuity]]; or [[#References|[a2]]].

Strongly countably complete topological spaces were introduced by Z. Frolík, [[#References|[a1]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  Z. Frolík,   "Baire spaces and some generalizations of complete metric spaces"  ''Czech. Math. J.'' , '''11'''  (1961)  pp. 237–248</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  I. Namioka,   "Separate continuity and joint continuity"  ''Pacific J. Math.'' , '''51'''  (1974)  pp. 515–531</TD></TR></table>