A note on star Lindelöf, first countable and normal spaces

Title:

A note on star Lindelöf, first countable and normal spaces

Creator:

Xuan, Wei-Feng

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1bde259c-7893-4c67-86c0-f995c4e288df
uuid:1bde259c-7893-4c67-86c0-f995c4e288df
doi:10.21136/MB.2017.0012-17

Subject:

star Lindelöf space, first countable space, normal space, and countable extent

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A topological space X is said to be star Lindelöf if for any open cover U of X there is a Lindelöf subspace A ⊂ X such that St(A, U) = X. The “extent” e(X) of X is the supremum of the cardinalities of closed discrete subsets of X. We prove that under V = L every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under MA + ¬CH, which shows that a star Lindelöf, first countable and normal space may not have countable extent.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

445-448

Source:

Mathematica bohemica | 2017 Volume:142 | Number:4

Harvested from:

CDK

Metadata only:

false