Proceedings of the Japan Academy, Series A, Mathematical Sciences

Dimension of the square of a compactum and local connectedness

Katsuya Yokoi

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Abstract

We state that a locally $(n-1)$-connected compactum with integral cohomological dimension $n$ has $n$-cohomological dimension modulo $p$ for some prime $p$. As a consequence, the integral cohomological dimension of the square of such a space is $2n$. In particular, the dimension of the square of an $n$-dimensional, locally $(n-1)$-connected compactum is $2n$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 6 (2002), 69-71.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392676

Digital Object Identifier
doi:10.3792/pjaa.78.69

Mathematical Reviews number (MathSciNet)
MR1913932

Zentralblatt MATH identifier
1039.54018

Subjects
Primary: 55M10: Dimension theory [See also 54F45]

Keywords
Dimension cohomological dimension locally connected

Citation

Yokoi, Katsuya. Dimension of the square of a compactum and local connectedness. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 6, 69--71. doi:10.3792/pjaa.78.69. https://projecteuclid.org/euclid.pja/1148392676


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