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A completely regular topological space $X$ is called a $P$-space if every zero-set in $X$ is open. An intermediate ring is a ring $A(X)$ of real-valued continuous functions on $X$ containing all the bounded continuous functions. In this paper, we find new characterizations of $P$-spaces $X$ in terms of properties of correspondences between ideals in $A(X)$ and $z$-filters on $X$. We also show that some characterizations of $P$-spaces that are described in terms of properties of $C(X)$ actually characterize $C(X)$ among intermediate rings on $X$.

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Murray, Will -  Sack, Joshua -  Watson, Saleem - 

Id.: 70963370

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveRings of continuous functions - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2017 Rocky Mountain Mathematics Consortium

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0035-7596

Fecha de contribución: 04-feb-2018


* Rocky Mountain J. Math. 47, no. 8 (2017), 2757-2775
* doi:10.1216/RMJ-2017-47-8-2757

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