Glasnik Matematicki, Vol. 55, No. 1 (2020), 129-142.

APPROXIMATE INVERSE LIMITS AND (M,N)-DIMENSIONS

Matthew Lynam and Leonard R. Rubin

Department of Mathematics, East Central University, Ada, Oklahoma 74820, USA
e-mail: mlynam@ecok.edu

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. Here we are going to look at this concept in the setting of approximate inverse systems of compact metric spaces. We give a characterization of (m,n)-dim X, where X is the limit of an approximate inverse system, strictly in terms of the given system.

2010 Mathematics Subject Classification.   54F45

Key words and phrases.   Dimension, (m,n)-dim , approximate inverse system

https://doi.org/10.3336/gm.55.1.11

References:

1. R. Engelking, Theory of dimensions finite and infinite, Heldermann Verlag, Lemgo, 1995.
   MathSciNet    

2. V. V. Fedorchuk, Finite dimensions defined by means of m-coverings, Mat. Vesnik 64 (2012), 347-360.
   MathSciNet    

3. V. V. Fedorchuk, Estimates of the dimension (m,n)-dim, Mosc. Univ. Math. Bull. 68 (2013), 177-181.
   MathSciNet     CrossRef

4. V. V. Fedorchuk, Inductive (m,n)-dimensions, Topology Appl. 169 (2014), 120-135.
   MathSciNet     CrossRef

5. V. Fedorchuk, Valuations for dimension (m,n)-dim, Matem. Vestnik, MUS (2013) (in Russian), in press.

6. M. Lynam and L. R. Rubin, Extensional maps and approximate inverse limits, Topology Appl. 239 (2018), 324-336.
   MathSciNet     CrossRef

7. S. Mardešić and L. R. Rubin, Approximate inverse systems of compacta and covering dimension, Pacific J. Math. 138 (1989), no. 1, 129-144.
   MathSciNet     CrossRef

8. S. Mardešić and J. Segal, 𝒫-like continua and approximate inverse limits, Math. Japon. 33 (1988), no. 6, 895-908.
   MathSciNet    

9. N. Martynchuk, Factorization theorem for the dimension (m,n)-dim, Mosc. Univ. Math. Bull. 68 (2013), 188-191.
   MathSciNet     CrossRef

10. N. Martynchuk, Transfinite extension of dimension function (m,n)-dim, Topology Appl. 160 (2013), 2514-2522.
    MathSciNet     CrossRef

11. N. Martynchuk, Several remarks concerning (m,n)-dimensions, Topology Appl. 178 (2014), 219-229.
    MathSciNet     CrossRef

12. N. Martynchuk, Theorem on universal spaces for dimension function (m,n)-dim, Mat. Zametki (2013), in press.