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## Fundamenta Mathematicae

1993 | 142 | 3 | 241-255
Tytuł artykułu

### On approximate inverse systems and resolutions

Autorzy
Treść / Zawartość
Warianty tytułu
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
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
241-255
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-05-05
poprawiono
1992-10-28
Twórcy
autor
• Department of Mathematics, University of Zagreb, Bijenička Cesta 30, 41000 Zagreb, Croatia
Bibliografia
• [1] M. G. Charalambous, Approximate inverse systems of uniform spaces and an application of inverse systems, Comment. Math. Univ. Carolin. 32 (1991), 551-565.
• [2] I. Lončar, Some results on resolution of spaces, Rad Jugosl. Akad. Znan. Umjet. Mat. Znan. 428 (6) (1987), 37-49.
• [3] S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53-78.
• [4] S. Mardešić and V. Matijević, P-like spaces are limits of approximate P-resolutions, Topology Appl. 45 (1992), 189-202.
• [5] S. Mardešić and L. R. Rubin, Approximate inverse systems of compacta and covering dimension, Pacific J. Math. 138 (1989), 129-144.
• [6] S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam 1982.
• [7] S. Mardešić and T. Watanabe, Approximate resolutions of spaces and mappings, Glas. Mat. 24 (1989), 583-633.
• [8] V. Matijević and N. Uglešić, A new approach to the theory of approximate resolutions, preprint.
• [9] T. Watanabe, Approximative shape I, Tsukuba J. Math. 11 (1987), 17-59.
• [10] T. Watanabe, Approximate resolutions and covering dimension, Topology Appl. 38 (1991), 147-154.
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Bibliografia
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