Tychonoff expansions with prescribed resolvability properties
نویسندگان
چکیده
Article history: Received 22 January 2009 Accepted 1 December 2009 MSC: primary 05A18, 03E05, 54A10 secondary 03E35, 54A25, 05D05
منابع مشابه
Resolvability properties via independent families
The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω < λ κ , no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a s...
متن کاملResolvability: a selective survey and some new results
Following guidance from the Organizing Committee, the authors give a brief introduction to the theory of spaces which are resolvable in the sense introduced by Hewitt (1943). The new results presented here are these. (A) A countably compact regular Hausdorff space without isolated points is w-resolvable--that is, it admits an infinite family of pairwise disjoint dense subsets. (B) Among Tychono...
متن کاملEigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....
متن کاملReal Analysis Quals - Helpful Information
2.1. Basic properties: separation, countability, separability, compactness, connectedness. A space X is Tychonoff if for u, v ∈ X, there exists a neighborhood of u not containing v (and by symmetry a neighborhood of v not containing u). It is Hausdorff if every two points can be separated by disjoint neighborhoods. It is regular if it is Tychonoff and every closed set and point not in the set c...
متن کاملo-Boundedness of free objects over a Tychonoff space
In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...
متن کامل