Baire spaces, Tychonoff powers and the Vietoris topology
Cao, J; Tomita, AH
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In this paper, we show that if the Tychonoﬀ power Xω of a quasiregular space X is Baire, then its Vietoris hyperspace 2X is also Baire. We also provide two examples to show (i) the converse of this result does not hold in general, and (ii) the Baireness of ﬁnite powers of a space is insuﬃcient to guarantee the Baireness of its hyperspace.