Vietoris continuous selections on scattered spaces
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Abstract
We prove that a countable regular space has a continuous selection if D and only if it is scattered. Further we prove that a paracompact scattered space admits a continuous selection if each of its points has a countable pseudobase. We also provide two examples to show that: (1) paracompactness can not be replaced by countable compactness even together with (collectionwise) normality, and (2) having countable pseudobase at each of its points can not be omitted even in the class of regular Lindelöf linearly ordered spaces.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 54(2), 273281, 200204
The Mathematical Society of Japan