Geodesic
Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces
Filomat, Tome 35 (2021) no. 5, p. 1431

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DOI

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.
DOI : 10.2298/FIL2105431S
Classification : 54E05, 54F45
Keywords: Brouwer dimension, proximity inductive dimension, proximity 
Jeremy Siegert. Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces. Filomat, Tome 35 (2021) no. 5, p. 1431 . doi: 10.2298/FIL2105431S
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     author = {Jeremy Siegert},
     title = {Proximity inductive dimension and {Brouwer} dimension agree on compact {Hausdorff} spaces},
     journal = {Filomat},
     pages = {1431 },
     year = {2021},
     volume = {35},
     number = {5},
     doi = {10.2298/FIL2105431S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2105431S/}
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