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2002•Fundamenta MathematicaeRequires access

On typical parametrizations of finite-dimensional compacta on the Cantor set

P. Milewski

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Abstract

We prove that if $X$ is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto $X$, the set of points of maximal order is uncountable. Moreover, if $X$ is a perfect compactum of positive finite dimension

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What this paper is about

We prove that if $X$ is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto $X$, the set of points of maximal order is uncountable. Moreover, if $X$ is a perfect compactum of positive finite dimension

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Available abstract

We prove that if $X$ is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto $X$, the set of points of maximal order is uncountable. Moreover, if $X$ is a perfect compactum of positive finite dimension

Key concepts: Uncountable set, Mathematics, Cantor set, Surjective function, Dimension (graph theory), Cantor function, Finite set, Countable set

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