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A continuous homomorphism of a thin set onto a fat set

  • Authors: Chalebgwa, Taboka , Morris, Sidney
  • Date: 2022
  • Type: Text , Journal article
  • Relation: Bulletin of the Australian Mathematical Society Vol. 106, no. 3 (2022), p. 500-503
  • Full Text: false
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  • Description: A thin set is defined to be an uncountable dense zero-dimensional subset of measure zero and Hausdorff measure zero of an Euclidean space. A fat set is defined to be an uncountable dense path-connected subset of an Euclidean space which has full measure, that is, its complement has measure zero. While there are well-known pathological maps of a set of measure zero, such as the Cantor set, onto an interval, we show that the standard addition on

Transversality, regularity and error bounds in variational analysis and optimisation

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