Journal of the Mathematical Society of Japan

The strange aspect of most compacta

Tudor ZAMFIRESCU

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Abstract

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

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

Dates
First available in Project Euclid: 14 September 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1158241930

Digital Object Identifier
doi:10.2969/jmsj/1158241930

Mathematical Reviews number (MathSciNet)
MR2139729

Zentralblatt MATH identifier
1101.54032

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

Keywords
Baire categories compacta continua starshaped sets

Citation

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


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