Baire spaces and hyperspaces
نویسندگان
چکیده
منابع مشابه
Baire Spaces, Sober Spaces
In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:
متن کاملA note on Volterra and Baire spaces
In Proposition 2.6 in (G. Gruenhage, A. Lutzer, Baire and Volterra spaces, textit{Proc. Amer. Math. Soc.} {128} (2000), no. 10, 3115--3124) a condition that every point of $D$ is $G_delta$ in $X$ was overlooked. So we proved some conditions by which a Baire space is equivalent to a Volterra space. In this note we show that if $X$ is a monotonically normal $T_1...
متن کاملProducts of Baire Spaces
Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...
متن کاملBaire Spaces , Sober Spaces 1 Andrzej
In the article concepts and facts necessary to continue formalization of theory of continuous lattices according to [11] are introduced. and [4] provide the notation and terminology for this paper. 1. PRELIMINARIES The following two propositions are true: (1) For all sets X, A, B such that A ∈ Fin X and B ⊆ A holds B ∈ Fin X. (2) For every set X and for every family F of subsets of X such that ...
متن کاملUniform Properties and Hyperspaces of Metrizable Spaces
Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1975
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1975.58.133