On approximate inverse systems and resolutions

• Autorzy: Sibe Mardešić
• Języki publikacji: EN

Abstrakty

EN

Recently, L. R. Rubin, T. Watanabe and the author have introduced approximate inverse systems and approximate resolutions, a new tool designed to study topological spaces. These systems differ from the usual inverse systems in that the bonding maps $p_{aa'}$ are not subject to the commutativity requirement $p_{aa' p_{a'a''} = p_{aa''}, a ≤ a' ≤ a''$. Instead, the mappings $p_{aa'}p_{a'a''}$ and $p_{aa''}$ are allowed to differ in a way controlled by coverings $U_a$, called meshes, which are associated with the members $X_a$ of the system. The purpose of this paper is to consider a more general and much simpler notion of approximate system and approximate resolution, which does not require meshes. The main result is a construction which associates with any approximate resolution in the new sense an approximate resolution in the previous sense in such a way that previously obtained results remain valid in the present more general setting.

Słowa kluczowe

EN

inverse system; approximate inverse system; inverse limit; resolution; approximate resolution; dimension

Kategorie tematyczne

• 54B35: Spectra
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 142
• Numer: 3
• Strony: 241-255

Daty

wydano

1993

otrzymano

1992-05-05

poprawiono

1992-10-28

Twórcy

autor

Sibe Mardešić

• Department of Mathematics, University of Zagreb, Bijenička Cesta 30, 41000 Zagreb, Croatia

Bibliografia

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• [7] S. Mardešić and T. Watanabe, Approximate resolutions of spaces and mappings, Glas. Mat. 24 (1989), 583-633.
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