Abstract:
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.