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On the Stone-Čech bicompactification of a bispace

Part of: Maps and general types of spaces defined by maps Fairly general properties Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

S. Garcia-Ferreira ,
S. Romaguera  and
M. Sanchis
S. Garcia-Ferreira
Affiliation:
Instituto de Mathemáticas, Ciudad Universitaria (UNAM), 04510, México D.F., México e-mail: sgarcia@zeus.ccu.umich.mx
S. Romaguera
Affiliation:
Escuela de Caminos, Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain e-mail: sromague@mat.upv.es
M. Sanchis
Affiliation:
Department de Mathemàtiques, Universitat Jaume I, Campus del Riu Sec, 12071 Castelló, Spain e-mail: sanchis@mat.uji.es
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Abstract

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In this paper we study the Stone-Čech bicompactification () of the bispace (X, P, Q). We show that the ring of all continuous real-valued functions on () may be identified with the uniform closure of a suitable subring of C(). Using this result, we give a characterization of the Wallman-Sanin compactifications of the pairwise Tychonoff bitopological spaces.

Keywords

BispaceWallman-Sanin compactificationStone-Čech bicompactificationequivalent compactificationsbicontinuous function

MSC classification

Secondary: 54C20: Extension of maps 54C30: Real-valued functions 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54E50: Complete metric spaces 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 358 - 372
Copyright
Copyright © Australian Mathematical Society 1999

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