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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Numerical meshes and covering meshes of approximate inverse systems of compacta


Author: Tadashi Watanabe
Journal: Proc. Amer. Math. Soc. 123 (1995), 959-962
MSC: Primary 54B35; Secondary 54F45
MathSciNet review: 1254858
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Abstract: Mardešić and Rubin (1989) introduced approximate inverse systems of metric compacta by the conditions $ {({\text{A}}1)^ \ast } - {({\text{A}}3)^ \ast }$. Mardešić and Watanabe (1988) introduced approximate inverse systems of topological spaces by the conditions $ ({\text{A}}1) - ({\text{A}}3)$. In this note we show that any approximate inverse system of metric compacta satisfies $ ({\text{A}}1) - ({\text{A}}3)$ if and only if it satisfies $ {({\text{A}}1)^\ast} - {({\text{A}}3)^\ast}$ for some matrices (see Theorem 1).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1254858-5
PII: S 0002-9939(1995)1254858-5
Keywords: Inverse system, approximate inverse system
Article copyright: © Copyright 1995 American Mathematical Society