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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 551=26, 2022.

Original scientific paper

https://doi.org/10.21857/yq32ohxj09

Inverse systems of compact Hausdorff spaces and (m,n)-dimension

Matthew Lynam ; Department of Mathematics, East Central University, Ada, Oklahoma 74820, USA
Leonard R. Rubin orcid id orcid.org/0000-0002-1108-0267 ; Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

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Abstract

In 2012, V. Fedorchuk, using m-pairs and n-partitions, introduced the notion of the (m, n)-dimension of a space. It generalizes covering dimension; Fedorchuk showed that (m, n)-dimension is preserved in inverse limits of compact Hausdorff spaces. We separately have characterized those approximate inverse systems of compact metric spaces whose limits have a specified (m, n)-dimension. Our characterization is in terms of internal properties of the system. Here we are going to give a parallel internal characterization of those inverse systems of compact Hausdorff spaces whose limits have a specified (m, n)-dimension. Fedorchuk's limit theorem will be a corollary to ours.

Keywords

Dimension; m-pair; (m, n)-dimension; n-partition; inverse system

Hrčak ID:

283955

URI

https://hrcak.srce.hr/283955

Publication date:

27.9.2022.

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