2019•arXiv (Cornell University)Open access
Proximity inductive dimension and Brouwer dimension agree on compact\n Hausdorff spaces
Jeremy Siegert
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Abstract
In this paper we show that the proximity inductive dimension defined by\nIsbell agrees with the Brouwer dimension originally described by Brouwer on the\nclass of compact Hausdorff spaces. Consequently, Fedorchuk's example of a\ncompact Hausdorff space whose Brouwer dimension exceeds its Lebesgue covering\ndimension is an example of a space whose proximity inductive dimension exceeds\nits proximity dimension as defined by Smirnov.\n
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