Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 189-199.

INVERSE SYSTEMS OF COMPACT HAUSDORFF SPACES AND (m, n)-DIMENSION

Matthew Lynam and Leonard R. Rubin

Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
e-mail: lrubin@ou.edu

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.

2020 Mathematics Subject Classification.   54F45.

Key words and phrases.   Dimension, m-pair, (m, n)-dimension, n-partition, inverse system.

DOI: https://doi.org/10.21857/yq32ohxj09

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