منابع مشابه
On the Baire Category Theorem
Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...
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 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 کاملOn Baire and Harmonic Functions
We consider two spaces of harmonic functions. First, the space H(U) of functions harmonic on a bounded open subset U of R and continuous to the boundary. Second, the space H0(K) of functions on a compact subset K of R n which can be harmonically extended on some open neighbourhood of K. A bounded open subset U of R is called stable if the space H(U) is equal to the uniform closure of H0(U ). We...
متن کاملBaire Reflection
We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of ω2, such as the principle asserting that any point countable Baire space has a stationary set of closed subspaces of weight ω1 which are also Baire spaces. These principles entail the analogous principles of stationary reflection but are incompatible with forc...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2000
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00100-5