Algebras and spaces of dense constancies

Title:

Algebras and spaces of dense constancies

Creator:

Bella, Angelo, Martinez, Jorge, and Woodward, Scott D.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c2914fda-3502-4cb0-aadf-834ed7390de0
uuid:c2914fda-3502-4cb0-aadf-834ed7390de0

Subject:

space and algebra of dense constancy and $c$-spectrum

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A DC-space (or space of dense constancies) is a Tychonoff space $X$ such that for each $f\in C(X)$ there is a family of open sets $\lbrace U_i\: i\in I\rbrace $, the union of which is dense in $X$, such that $f$, restricted to each $U_i$, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean $f$-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property.

Language:

English

Rights:

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

Coverage:

449-461

Source:

Czechoslovak Mathematical Journal | 2001 Volume:51 | Number:3

Harvested from:

CDK

Metadata only:

false