Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2005; 42(2): 291-304

Printed March 1, 2005

Copyright © The Korean Mathematical Society.

Cauchy completion of Csaszar frames

Se Hwa Chung

Kyungwon University

Abstract

We introduce a concept of Cauchy complete Cs\'{a}sz\'{a}r frames and construct Cauchy completions of Cs\'{a}sz\'{a}r frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

Keywords: frame, frame homomorphism, Cs$\acute{a}$sz$\acute{a}$r frame, Cauchy complete Cs\'{a}sz\'{a}r frame, Cauchy completion, uniform Cs\'{a}sz\'{a}r frame, Cauchy homomorphism, uniform homomorphism, regular Cauchy filter

MSC numbers: 06D99, 18A40, 54A15, 54D35