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A study of chain conditions and dually properties.
- Source :
-
Topology & Its Applications . Mar2019, Vol. 254, p39-49. 11p. - Publication Year :
- 2019
-
Abstract
- Abstract In this paper, we make some observations on chain conditions and dually properties. In particular, we show that: (1) A subspace X ⊂ ω 1 ω is dually CCC then e (X) ≤ ω and a normal subspace X ⊂ ω 1 ω is DCCC if and only if e (X) ≤ ω ; (2) There is a Tychonoff pseudocompact subspace X ⊂ (ω 1 + 1) 2 which is not dually CCC; (3) In the class of o-semimetrizable spaces, dually separable is self-dual with respect to neighbourhood assignments. As an application, we obtain an example of a CCC normal Moore space which is not dually separable under MA+¬CH; (4) There exists an example of a large normal CCC semi-stratifiable space, which answers a question of Xuan and Song (2018) [21, Question 4.11] ; (5) Every dually separable and monotonically monolithic space is Lindelöf, which gives a partial answer to a question of Alas, Junqueira, van Mill, Tkachuk and Wilson (2011) [2, Question 2.1] ; (6) A dually separable Hausdorff space with a strong rank 1-diagonal has cardinality at most 2 c. The conclusion is also true for regular spaces if we replace "strong rank 1-diagonal" with " G δ -diagonal"; (7) A dually separable ω -monolithic Hausdorff space with a G δ -diagonal has cardinality at most c. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01668641
- Volume :
- 254
- Database :
- Academic Search Index
- Journal :
- Topology & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 134185023
- Full Text :
- https://doi.org/10.1016/j.topol.2018.12.009