In this paper, some partial solutions are given to the problem concerning θ-refinability of strict p-spaces. It is shown that every locally compact strict p-space is θ-refinable and every locally hereditarily separable strict p-space is subparacompact.
In this paper we study the notions of scannable spectrum and roll of a spectral tree, which appeared in slightly different form in [3] and [5] respectively. One of the main results: scannable spectra necessarily have fully closed projections and spectra of length ⩽ω with fully closed projections are scannable. The technique of scannable spectra is used, when we study the new class of fully separable spaces. We prove that the statement - every fully separable almost perfectly normal compact space has cardinality ⩽c-is independent of ZFC.
The non-manifold dog bone space of W.T. Eaton is modified to obtain a decomposition of Euclidean n-space, n≥3, into points and a null sequence of cellular sets so that the resulting decomposition space is not a manifold. Our construction follows a procedure given by R.J. Daverman who has proved this result for n≥5. Our construction has the advantage of working in all possible dimensions including the previously unknown dimension 4.
It is proved that if X is a (metric) continuum, if C(X) is the space of nonempty closed connected subsets of X with the Hausdorff metric, and if A1,…,An are members of C(X) such that each of the sets C(X)-{Ai} is arcwise connected, then C(X)-{A1,…,An} is arcwise connected.
In this paper we prove the existence of a universal element in the class of locally-finite dimensional metric spaces with weight τ. We also show that every locally finite dimensional metric space has uniformly zero-dimensional continuous mapping in a locally compact locally finite dimensional separable metric space.
A space X partitions a space Y if Y is the union of pairwise disjoint subjets, each of which is homeomorphic to X. We study the topological partition relation, particularly in the context of separable metric spaces, obtaining topological analogues to well-known problems in the theory of geometric partitions.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：