The weak and strong convergence in metrizable spaces over valued fields.
A Note on Metrizable Linear Topologies Strictly Finer than a Given Metrizable Complete Linear Topology.
On inductive limits of topological algebras
The Mackey-Arens and Hahn-Banach theorems for spaces over valued fields
Baire-like spaces C(X,E)
We characterize Baire-like spaces C(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.
Distinguished Fréchet spaces dual metric spaces and tightness conditions for .
The Mackey-Arens theorem for non-locally convex spaces.
Let R be a subcategory of the category of all topological vector spaces. Let E be an element of R. The problem of the existence of the finest R-topology on E with the same continuous linear functionals as the original one is discussed. Remarks concerning the Hahn-Banach Extension Property are included.
On suprema of metrizable vector topologies with trivial dual
A note on a theorem of Klee
It is proved that if are separable quasi-Banach spaces, then contains a dense dual-separating subspace if either or has this property.
Remarks on bounded sets in -spaces
We establish the relationship between regularity of a Hausdorff -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff -space to be an -space. A factorization theorem for -spaces with property (K) is also obtained.
Simple construction of spaces without the Hahn-Banach extension property
An elementary construction for an abundance of vector topologies on a fixed infinite dimensional vector space such that has not the Hahn-Banach extension property but the topological dual separates points of from zero is given.
On subspaces of ultrabornological spaces
Some remarks on -Baire-like and --Baire-like spaces
Unordered Baire-like spaces without local convexity.
The aim of the present paper is to study the class of tvs which we define by ommiting the word increasing in the definition of *-suprabarrelled spaces. We prove that the product of Baire tvs is *-UBL and hence the class of *-UBL spaces is stricty larger than the class of Baire spaces.
Locally convex topologies in linear orthogonality spaces
In this paper, we investigate the existence and characterizations of locally convex topologies in a linear orthogonality space.
A note on Fréchet-Urysohn locally convex spaces.
Recently Cascales, Kąkol and Saxon showed that in a large class of locally convex spaces (so called class G) every Fréchet-Urysohn space is metrizable. Since there exist (under Martin’s axiom) nonmetrizable separable Fréchet-Urysohn spaces C(X) and only metrizable spaces C(X) belong to class G, we study another sufficient conditions for Fréchet-Urysohn locally convex spaces to be metrizable.
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...
A non-archimedean Dugundji extension theorem
We prove a non-archimedean Dugundji extension theorem for the spaces of continuous bounded functions on an ultranormal space with values in a non-archimedean non-trivially valued complete field . Assuming that is discretely valued and is a closed subspace of we show that there exists an isometric linear extender if is collectionwise normal or is Lindelöf or is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace of an ultraregular...
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