Journal of the Mathematical Society of Japan

The strange aspect of most compacta


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In this paper we describe a compact set K in R d which is typical from the point of view of Baire categories, as it appears when seen from some point x of R d . It matters whether x belongs to K or not! If xK , then K looks porous (this is easily seen). If x K , then K looks only σ -porous, but dense at least in a half-sphere (of directions from x ). If x is a typical point of K , then K looks even dense (in the whole sphere).

Article information

J. Math. Soc. Japan, Volume 57, Number 3 (2005), 701-708.

First available in Project Euclid: 14 September 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54E52: Baire category, Baire spaces 54F15: Continua and generalizations 54D30: Compactness

Baire categories compacta continua starshaped sets


ZAMFIRESCU, Tudor. The strange aspect of most compacta. J. Math. Soc. Japan 57 (2005), no. 3, 701--708. doi:10.2969/jmsj/1158241930.

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