Baire spaces, Tychonoff Powers and the Vietoris topology

Jiling Cao and A. H. Tomita


In this paper, we show that if the Tychonoff power $X^omega$ of a quasi-regular space $X$ is Baire then its Vietoris hyperspace $2^X$ is also Baire. We provide two examples to show that the converse of this result does not hold in general, and the Baireness of finite powers of a space is insufficient to guarantee the Baireness of its hyperspace.

Baire space, Tychonoff power, Vietoris topology.

Math Review Classification
Primary 54E52 ; Secondary 54B10, 54B20, 91A05

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10 pages

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