On Cauchy Homomorphisms of Nearness Frames
作者:
B. Banaschewski,
A. Pultr,
期刊:
Mathematische Nachrichten
(WILEY Available online 1997)
卷期:
Volume 183,
issue 1
页码: 5-18
ISSN:0025-584X
年代: 1997
DOI:10.1002/mana.19971830102
出版商: WILEY‐VCH Verlag
关键词: Nearness frame;Completion;Cauchy homomorphisms;uniform and locally uniform homomorphisms
数据来源: WILEY
摘要:
AbstractTo include the pointfree case, the notion of a Cauchy map easily extends as the condition that the preimage of any regular Cauchy filter contains a regular Cauchy filter. This extension, however, can be unsatisfactory if the regular Cauchy filters are scarce or non‐existent, making the condition too weak, indeed sometimes even void. In this paper a variant of the notion, independent on the existence of any kind of filters, is studied: a homomorphism is called fully Cauchy if it lifts to the completions. This is generally stronger than, and in the spatial and metric cases it coincides with the previously mentioned property. Moreover, it is stable under localizatio
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