Year: 2011
Type: preprint
Abstract: We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1space). This answers the Problem 3 in [Arhangelskii, A.V. - Isler, R. - Tironi, G: On pseudo-radial spaces, Comment. Math. Univ. Carolin. 27 (1986), 137-156]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top. (The same result without any separation axiom was proved already in the master thesis E. Murtinová: Podprostory pseudoradiálních prostorů. I wasn't aware of this work when preparing this paper.)
Source: arXiv (Cornell University)
Author: Sleziak, Martin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1550197900