Subject: Algebraic Topology Discussion List Date: Tue, 27 Jul 2004 14:02:27 -0400 (EDT) From: David Groisser Two questions: 1. Let $M_{k,n}$ be the space of real $k\times n$ matrices, $k\geq n$. For use in a paper, I needed to compute (and have computed) the topology of the very non-Hausdorff space $M_{k,n}/GL(n,R)$ ($GL(n,R)$ acting by right-multiplication). Does anybody know if the topology of this space has appeared in print somewhere? I'd like to know if there's a reference I can or should cite. 2. (Related to first question.) Let $X$ be a topological space, not assumed to be $T_1$. For $p\in X$, let $U_p$ be the intersection of all open neighborhoods of $p$. Is there a standard name for $U_p$? If there isn't a standard name in complete generality, is there a standard name under the assumption that $X$ is $T_0$? If there's no standard name, I've considered the names "spread(p)", "blur(p)", and "touch(p)". Any comments on the suitability/unsuitability of these names, or suggestions for better ones, would be welcome. ---------------------------------------------------------------------- David Groisser | groisser@math.ufl.edu | Department of Mathematics | (352)392-0281 extension 261 | University of Florida | fax (352)392-8357 | 364 Little Hall | http://www.math.ufl.edu/~groisser | PO Box 118105 | | Gainesville, FL 32611-8105 | | ----------------------------------------------------------------------