On the metrizability of spaces with a sharp base
| dc.creator | Good, Chris | |
| dc.creator | Knight, Robin W. | |
| dc.creator | Mohamad, Abdul M. | |
| dc.date | 2002-04-10 | |
| dc.date.accessioned | 2026-07-07T04:47:34Z | |
| dc.date.available | 2026-07-07T04:47:34Z | |
| dc.description | A base $\mathcal{B}$ for a space $X$ is said to be sharp if, whenever $x\in X$ and $(B_n)_{n\inω}$ is a sequence of pairwise distinct elements of $\mathcal{B}$ each containing $x$, the collection $\{\bigcap_{j\le n}B_j:n\inω\}$ 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0204127 | |
| dc.identifier | http://arxiv.org/abs/math/0204127 | |
| dc.identifier | Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001), pp. 125--134, Topology Atlas, Toronto, 2002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63770 | |
| dc.subject | General Topology | |
| dc.subject | 54E20, 54E30 | |
| dc.title | On the metrizability of spaces with a sharp base | |
| dc.type | text |