Strongly countably complete topological space
From Encyclopedia of Mathematics
A topological space 
for which there is a sequence 
of open coverings of 
such that a sequence 
of closed subsets of 
has a non-empty intersection whenever 
for all 
and each 
is a subset of some member of 
.
Locally countably compact spaces and Čech-complete spaces are strongly countably complete. Every strongly countably complete space is a 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 
implies joint continuity on a large subset of 
, see Namioka space; Namioka theorem; Separate and joint continuity; or [a2].
Strongly countably complete topological spaces were introduced by Z. Frolík, [a1].
References
| [a1] | Z. Frolík, "Baire spaces and some generalizations of complete metric spaces" Czech. Math. J. , 11 (1961) pp. 237–248 |
| [a2] | I. Namioka, "Separate continuity and joint continuity" Pacific J. Math. , 51 (1974) pp. 515–531 |
How to Cite This Entry:
Strongly countably complete topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strongly_countably_complete_topological_space&oldid=32427
Strongly countably complete topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Strongly_countably_complete_topological_space&oldid=32427
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article