1. CMB Online first
|Free Locally Convex Spaces and the $k$-space Property|
Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. Then $L(X)$ is a $k$-space if and only if $X$ is a countable discrete space. We prove also that $L(D)$ has uncountable tightness for every uncountable discrete space $D$.
Keywords:free locally convex space, $k$-space, countable tightness
Categories:46A03, 54D50, 54A25
2. CMB 2010 (vol 53 pp. 286)
|Orders of π-Bases|
We extend the scope of B. Shapirovskii's results on the order of $\pi$-bases in compact spaces and answer some questions of V. Tkachuk.
Keywords:Shapirovskii π-base, point-countable π-base, free sequences, canonical form for ordinals
Categories:54A25, 03E10, 03E75, 54A35