
Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces
Author(s) -
Jeremy Siegert
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2105431s
Subject(s) - inductive dimension , packing dimension , hausdorff dimension , mathematics , dimension function , effective dimension , minkowski–bouligand dimension , dimension (graph theory) , dimension theory (algebra) , lebesgue covering dimension , complex dimension , pure mathematics , lebesgue integration , discrete mathematics , mathematical analysis , fractal dimension , fractal
We show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer (for Polish spaces without isolated points) on the class of compact Hausdorff spaces. This shows that Fedorchuk?s example of a compact Hausdorff space whose Brouwer dimension exceeds its Lebesgue covering dimension is an example of a space whose proximity inductive dimension exceeds its proximity dimension as defined by Smirnov. This answers Isbell?s question of whether or not proximity inductive dimension and proximity dimension coincide.