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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 3, 2020, pp. 277–288
DOI: 10.4171/ZAA/1660

Published online: 2020-07-06

On Some Generic Small Cantor Spaces

Emma D'Aniello[1] and Martina Maiuriello[2]

(1) Università degli Studi della Campania, Caserta, Italy
(2) Università degli Studi della Campania, Caserta, Italy

Let $X = [0, 1]^n, n \geq 1$. We show that the typical (in the sense of Baire category) compact subset of $X$ is not only a zero dimensional Cantor space but it satisfies the property of being strongly microscopic, which is stronger than dimension zero.

Keywords: Microscopic set, Cantor space, Baire category, Hausdorff dimension

D'Aniello Emma, Maiuriello Martina: On Some Generic Small Cantor Spaces. Z. Anal. Anwend. 39 (2020), 277-288. doi: 10.4171/ZAA/1660