Two unrelated results involving Baire spaces
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:
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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 کاملQuestions on generalised Baire spaces
When studying questions about real numbers, it is common practice in set theory to investigate the closely related Baire space ω and Cantor space 2 . These spaces have been extensively studied by set theorists from various points of view, e.g., questions about cardinal characteristics of the continuum, descriptive set theory and other combinatorial questions. Furthermore, the investigation of 2...
متن کاملThe Geometry of Baire Spaces
We introduce the concept of Baire embeddings and we classify them up to C conjugacies. We show that two such embeddings are Cequivalent if and only if they have exponentially equivalent geometries. Next, we introduce the class of IFS-like Baire embeddings and we also show that two Hölder equivalent IFS-like Baire embeddings are C conjugate if and only if their scaling functions are the same. In...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0346761-6