convex set

(redirected from Absolutely convex)

convex set

[′kän‚veks ′set]
(mathematics)
A set which contains the entire line segment joining any pair of its points.
References in periodicals archive ?
n] is a sequence of closed, absolutely convex neighborhoods of zero so that U = [[intersection].
n]) of absolutely convex neighborhoods of zero in (E, [[tau].
There exists a non-complete real normed space whose totally antiproximinal absolutely convex subsets are not rare.
Since the closure B = cl(S(a)) is a closed, idempotent, bounded and absolutely convex subset in A (see, for example, [27], pp.
6) The absolutely convex hull of S [subset] A is the set
An absolutely convex subset of a locally convex algebra (E, [tau]) is said to be bornivorous (resp.
Otherwise there is an absolutely convex neighborhood of the origin U in (E',[sigma] (E', E)) and a strictly increasing sequence {[n.
An absolutely convex subset of (E, [tau]) is said to be bornivorous (resp.
If every absolutely convex, closed and bounded subset of the vector subspace F of E is locally compact, then F endowed with the [rho](E, E')-topology is a (LB)-space, where [rho](E, E') designates the topology on E of the uniform convergence on the absolutely convex compact subsets of E'.
Let B be a closed absolutely convex absorbing subset of [E.
0](E) and B(E) stand for the families of all absolutely convex 0-neighborhoods and absolutely convex bounded sets in E, respectively.