FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 3-18

On disjoint sums in the lattice of linear topologies

V. I. Arnautov
K. M. Filippov

Abstract

View as HTML     View as gif image

Let M be a vector space over a skew-field equipped with the discrete topology, $ \mathcal L(M) $ be the lattice of all linear topologies on M ordered by inclusion, and $ t*, t0, t1 Î \mathcal L(M) $. We write $ t1 = t* \sqcup t0 $ or say that t1 is a disjoint sum of t* and t0 if t1 = inf{t0, t*} and sup{t0, t*} is the discrete topology.

Given $ t1, t0 Î \mathcal L(M) $, we say that t0 is a disjoint summand of t1 if $ t1 = t* \sqcup t0 $ for a certain $ t* Î \mathcal L(M) $. Some necessary and some sufficient conditions are proved for t0 to be a disjoint summand of t1.

Main page Contents of the journal News Search

Location: http://mech.math.msu.su/~fpm/eng/k03/k031/k03101h.htm
Last modified: April 4, 2004.