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Problem 909 — Erdős Problems

Problem 909

Let $n\geq 2$ . Is there a space $S$ of dimension $n$ such that $S^2$ also has dimension $n$ ?

Source: erdosproblems.com/909

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An accepted solution exists. The statement is true.

Proved, on the site's label, which credits Anderson and Keisler's 1967 construction for the general case; see the claim page (Anderson and Keisler, 1967).

AnKe67: Anderson, R. D. and Keisler, J. E., An example in dimension theory. Proc. Amer. Math. Soc. 18 (1967), no. 4, 709--713, DOI 10.1090/S0002-9939-1967-0215288-0; the article is served free by the publisher.

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Status: Solved, Proved
Topics: Analysis
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In the wiki: Wiki page