Are all subsets of compact sets compact? Why is the empty set both open and closed? How to prove a set is compact? Prove that every finite set in R is compact. How do we know if a subset is compact? How to prove the countable product of compact sets is compact? If the subset of...
The author shows that for most compact starshaped set... T Zamfirescu - 《Aequationes Mathematicae》 被引量: 26发表: 1988年 Analytic, co-analytic and projective sets from Brouwer's intuitionistic perspective We first study analytic sets; these are the projections of the closed subsets of Baire...
Given a finite alphabet Σ, we give a simple characterization of those G δ subsets of Σω which are deterministic ω-regular (i.e. accepted by Büchi ... R Barua - 《Theoretical Computer Science》 被引量: 41发表: 1992年 Some generalizations of Fedorchuk duality theorem—I - ScienceDirec...
family (of countable subsets of ω1) is not countably metacompact. Assuming a situation when closed discrete sets are Gδ sets we show that any first countable, countably metacompact space, of countable scattered height, is developable....
[sigma]-algebra generated by zero-sets are called Baire sets and the elements of the [sigma]-algebra generated by closed sets are called Borel sets; B(X)and [B.sub.0](X) are the classes of Borel and Baire subsets of X and [M.sub.[sigma]](X) denotes the class of all scalar-...
Compact simplices (the compact convex sets where integral representations are unique) and related sets. 4. Exposed points and the Radon–Nikodým Property (RNP) (for Banach spaces and their convex subsets, also in the setting of complex convexity). 5. Boundaries and support points (including ...
In general, however, these topologies of closed subsets are not compact. In this paper, a topology of closed subsets of a topological space is constructed that is always compact. This topology is called the compact topology and has many pleasant features. For closed subsets of compact Hausdorff...
A compact zero-dimensional space is called h-homogeneous if all nonempty clopen subsets are homeomorphic. Equivalently, X is the Stone space of a homogeneo... E Glasner,Y Gutman - The universal minimal space of the homeomorphism group of a h-homogeneous space 被引量: 1发表: 2012年 加载...
Spaces whose feebly compact subspaces are closed subsetsR.M. StephensonJr
A countable product of separable topological spaces is separable (exercise). Given a family of non-empty sets (Xi)i ∈ I and a filter Fi on Xi for each i∈ I, we write ∏i∈IFi for the filter on ∏i ∈ I Xi with base given by the set of subsets of the form ∏i ∈ I Ai ...