Compact-calibres of regular and monotonically normal spaces
A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set wh...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011365 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp.,
point-finite) collection of nonempty open sets is countable. It
has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every disjoint (resp., discrete) collection of
nonempty open sets is countable. The relative strengths of these six conditions are determined for Moore spaces, regular first countable spaces, linearly-ordered spaces, and arbitrary regular spaces. It is shown that the relative strengths for spaces with point-countable bases are the same as those for Moore spaces, and the relative strengths for linearly-ordered spaces are the same
as those for arbitrary monotonically normal spaces. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |