Sequential completeness and regularityof inductive limits of webbed spaces
Any inductive limit of bornivorously webbed spaces is sequentially complete iff it is regular.
Small ball properties for Fréchet spaces.
We give characterizations of certain properties of continuous linear maps between Fréchet spaces, as well as topological properties on Fréchet spaces, in terms of generalizations of Behrends and Kadets small ball property.
Sobre espacios (LF) metrizables.
Solution of a problem of Grothendieck.
Some aspects of the modern theory of Fréchet spaces.
We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?.
Some Classes of Locally Convex Riesz Spaces
Some examples on quasi-barrelled spaces
The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled -space containing a subspace of infinite countable codimension which is not -space, and bornological barrelled space which is not inductive limit of Baire space.
Some General Methods for Constructing Stable Convex Sets.
Some metric and topological properties of certain linear spaces of measurable functions
Some normability conditions on Fréchet spaces.
We define two new normability conditions on Fréchet spaces and announce some related results.
Some properties of short exact sequences of locally convex Riesz spaces
We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces.
Some remarks on almost radiality in function spaces
Some Remarks on the Weak Topology of Locally Convex Spaces
Sous-espaces fermés de séries universelles sur un espace de Fréchet
We improve a result of Charpentier [Studia Math. 198 (2010)]. We prove that even on Fréchet spaces with a continuous norm, the existence of only one restrictively universal series implies the existence of a closed infinite-dimensional subspace of restrictively universal series.
Spaces of Whitney jets on self-similar sets
It is shown that complemented subspaces of s, that is, nuclear Fréchet spaces with properties (DN) and (Ω), which are 'almost normwise isomorphic' to a multiple direct sum of copies of themselves are isomorphic to s. This is applied, for instance, to spaces of Whitney jets on the Cantor set or the Sierpiński triangle and gives new results and also sheds new light on known results.
Spectrum and Envelope of Holomorphy for Infinite Dimensional Riemann Domains.
Standard exact projective resolutions relative to a countable class of Fréchet spaces
We will show that for each sequence of quasinormable Fréchet spaces there is a Köthe space λ such that and there are exact sequences of the form . If, for a fixed ℕ, is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form . The result has some applications in the theory of the functor in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
Stochastic Basis in Fréchet Space.
Strictly convex spheres in V-spaces
Strictly extreme and strictly exposed points.