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Approximate inverse
systems of compacta and covering dimension
Sibe Mardesic and Leonard Rubin |
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Vol. 138 (1989), No. 1, 129–144
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Abstract |
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Approximate inverse systems of metric compacta are introduced and studied. The bonding maps in these systems commute only up to certain controlled values. With every such system X = (Xa,𝜖a,paa′,A) are associated a limit space X and projections pa : X → Xa. A compact Hausdorff space X has covering dimension dimX ≤ n if and only if it can be obtained as the limit of an approximate inverse system of compact polyhedra of dimension ≤ n. The analogous statement for usual inverse systems is known to be false. |
Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54B25
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Milestones
Received: 13 May 1987
Revised: 3 May 1988
Published: 1 May 1989
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Authors |
| Sibe Mardesic | |
| Leonard Rubin | |
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