Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 299-318.

CHARACTERIZING STRONG INFINITE-DIMENSION, WEAK INFINITE-DIMENSION, AND DIMENSION IN INVERSE SYSTEMS

Matthew Lynam and Leonard R. Rubin

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

Abstract.   We present internal characterizations for an inverse system of compact Hausdorff spaces that show when its limit will be strongly infinite-dimensional, weakly infinite-dimensional, or have its dimension dim ∈ N_{≥ 0}. The technique involves essential families.

2020 Mathematics Subject Classification.   54F45.

Key words and phrases.   Dimension, essential family, inverse system, strong infinite-dimension, weak infinite-dimension.

DOI: https://doi.org/10.21857/y54jof4wpm

References:

1. R. Engelking, General Topology, PWN-Polish Scientific Publishers, Warsaw, 1977.
   MathSciNet

2. L. Rubin, R. Schori and J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), 93-103.
   MathSciNet     CrossRef

3. L. Rubin, Hereditarily strongly infinite-dimensional spaces, Michigan Math. J. 27 (1980), 65-73.
   MathSciNet     CrossRef

4. L. Rubin, Noncompact hereditarily strongly infinite dimensional spaces, Proc. Amer. Math. Soc. 79 (1980), 153-154.
   MathSciNet     CrossRef

5. L. Rubin, Totally disconnected spaces and infinite cohomological dimension, Topology Proc. 7 (1982), 157-166.
   MathSciNet

6. L. Rubin, More compacta of infinite cohomological dimension, Contemp. Math. 44 (1985), 221-226.
   MathSciNet     CrossRef

7. K. Sakai, Geometric Aspects of General Topology, Springer Monographs in Mathematics, Springer, Tokyo, 2013.
   MathSciNet     CrossRef

8. J. Walsh, Infinite-dimensional compacta containing no n-dimensional (n ≥ 1) subsets, Topology 18 (1979), 91-95.
   MathSciNet     CrossRef