2002/04/10 by Chris Good, Robin W. Knight, Abdul M. Mohamad
Mathematics · #math.GN #msc:54E20 #msc:54E30
published as Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 125--134, Topology Atlas, Toronto, 2002 · 10 pages. Reprinted from Topology and its Applications, in press, Chris Good, Robin W. Knight and Abdul M. Mohamad, On the metrizability of spaces with a sharp base
arxiv created 2002/04/10 · arxiv updated 2009/11/30
A base B for a space X is said to be sharp if, whenever x∈ X and (Bn)n∈ω is a sequence of pairwise distinct elements of B each containing x, the collection \\bigcapj≤ nBj:n∈ω\ is a local base at x. We answer questions raised by Alleche et al. and Arhangel'ski\uı et al. by showing that a pseudocompact Tychonoff space with a sharp base need not be metrizable and that the product of a space with a sharp base and [0,1] need not have a sharp base. We prove various metrization theorems and provide a characterization along the lines of Ponomarev's for point countable bases.