Vietoris continuous selections on scattered spaces
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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 pseudo-base. 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 pseudo-base at each of its points can not be omitted even in the class of regular Lindelöf linearly ordered spaces.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 54(2), 273-281, 2002-04
The Mathematical Society of Japan