On nonregular ideals and $z^\circ$-ideals in $C(X)$

Title:

On nonregular ideals and $z^\circ$-ideals in $C(X)$

Creator:

Azarpanah, F. and Karavan, M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:6a6f19a1-b3d3-4e07-99a2-74009fc64f19
uuid:6a6f19a1-b3d3-4e07-99a2-74009fc64f19

Subject:

$z^\circ $-ideal, prime $z$-ideal, nonregular ideal, almost ${P}$-space, $\partial $-space, and $m$-space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The spaces $X$ in which every prime $z^\circ $-ideal of $C(X)$ is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces $X$, such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime $z^\circ $-ideal in $C(X)$ is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in $C(X)$ a $z^\circ $-ideal? When is every nonregular (prime) $z$-ideal in $C(X)$ a $z^\circ $-ideal? For instance, we show that every nonregular prime ideal of $C(X)$ is a $z^\circ $-ideal if and only if $X$ is a $\partial $-space (a space in which the boundary of any zeroset is contained in a zeroset with empty interior).

Language:

English

Rights:

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

Coverage:

397-407

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:2

Harvested from:

CDK

Metadata only:

false