Cardinalities of DCCC normal spaces with a rank 2-diagonal

Title:

Cardinalities of DCCC normal spaces with a rank 2-diagonal

Creator:

Xuan, Wei-Feng and Shi, Wei-Xue

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:791c73d6-0ab6-4c62-a11c-dd7ee1c146d5
uuid:791c73d6-0ab6-4c62-a11c-dd7ee1c146d5
doi:10.21136/MB.2016.0027-15

Subject:

cardinality, Discrete Countable Chain Condition, normal space, rank 2- diagonal, and Gδ-diagonal

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A topological space X has a rank 2-diagonal if there exists a diagonal sequence on X of rank 2, that is, there is a countable family {Un : n ∈ ω} of open covers of X such that for each x ∈ X, {x} = ∩ {St2 (x,Un): n ∈ ω}. We say that a space X satisfies the Discrete Countable Chain Condition (DCCC for short) if every discrete family of nonempty open subsets of X is countable. We mainly prove that if X is a DCCC normal space with a rank 2-diagonal, then the cardinality of X is at most c. Moreover, we prove that if X is a first countable DCCC normal space and has a Gδ-diagonal, then the cardinality of X is at most c.

Language:

English

Rights:

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

Coverage:

457-461

Source:

Mathematica bohemica | 2016 Volume:141 | Number:4

Harvested from:

CDK

Metadata only:

false