1. 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
2. CMB 2007 (vol 50 pp. 149)
|On Quotients of Non-Archimedean KÃ¶the Spaces |
We show that there exists a non-archimedean Fr\'echet-Montel space $W$ with a basis and with a continuous norm such that any non-archimedean Fr\'echet space of countable type is isomorphic to a quotient of $W$. We also prove that any non-archimedean nuclear Fr\'echet space is isomorphic to a quotient of some non-archimedean nuclear Fr\'echet space with a basis and with a continuous norm.
Keywords:Non-archimedean KÃ¶the spaces, nuclear FrÃ©chet spaces, pseudo-bases