On the three-space property for locally convex spaces.
On the Three-space-problem for df Spaces and Their Duals
On the three-space-problem for topological vector spaces.
On the topology of compactoid convergence in non-Archimedean spaces
On the ultrabornological property of the vector valued bounded function space.
On the Unicelluarity of l... (w).
On the Unimodality of Discrete Probability Measures.
On the upper envelopes of a family of -disjoint operators.
On the Wiener-Eberlein theorem
On the -dual of vector-valued sequence spaces of Maddox.
On Toeplitz sections in FK-spaces
On topological classification of non-archimedean Fréchet spaces
We prove that any infinite-dimensional non-archimedean Fréchet space is homeomorphic to where is a discrete space with . It follows that infinite-dimensional non-archimedean Fréchet spaces and are homeomorphic if and only if . In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .
On topological groups with a small base and metrizability
A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, , such that whenever β ≤ α for all . The class of all metrizable topological groups is a proper subclass of the class of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group is metrizable, and hence G is strictly angelic. We deduce from this result...
On topological, Lipschitz and uniform classification of LF-spaces
On Totally Barreled Spaces.
On two classes of LF-spaces
On variation topology
On vector lattices of elementary Carathéodory functions
In this paper we deal with the vector lattice of all elementary Carathéodory functions corresponding to a generalized Boolean algebra .
On vector measures
Let be the Banach space of real measures on a -ring , let be its dual, let be a quasi-complete locally convex space, let be its dual, and let be an -valued measure on . If is shown that for any there exists an element of such that for any and that the mapis order continuous. It follows that the closed convex hull of is weakly compact.
On vector spaces and algebras with maximal locally pseudoconvex topologies
Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological algebras,...