Infinite Set Totality

Author : William Johnston

Abstract : We present interesting comparisons of so-called “totalities'” of subsets of metric spaces of various types, such as a comparison between the totality of a subset of the reals $\mathbb{R}$ against the totality of a subset from the power set of the reals $\mathbb{P}(\mathbb{R})$. We use outer measure as one tool to define a set's totality, which can be constructed as a refinement of the set's cardinality and can then help clarify a foundational issue of real analysis.

Keywords : Comparing set totalities in metric spaces via outer measure

Conference Name : International Conference on Functional Analysis and Operator Theory (ICFAOT-26)

Conference Place : Edinburgh, UK

Conference Date : 11th Apr 2026