The Bade property and the λ-property in spaces of convergent sequences.
In this note we study the Bade property in the C(K,X) and c(X) spaces. We also characterize the spaces X = C(K,R) such that c(X) has the uniform λ-property.
The barrelled topology associated with the compact-open topology on H(U) and H(K)
The Bornological Topology on the Space of Holomorphic Mappings on a Banach Space.
The ...-Compact-Open Topology and its Relatives.
The density condition in projective tensor products.
In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.
The diametral dimension of the spaces of Whitney jets on sequences of points.
The dual of the space of holomorphic functions on locally closed convex sets.
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
The Finest Nachbin Topology is a Mixed Topology.
The non-archimedean space
The non-archimedian space BC(X) with the strict topology.
Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.
The non-pluripolarity of compact sets in complex spaces and the property for the space of germs of holomorphic functions
The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
The Oka-Weil theorem in locally convex spaces with the approximation property
The order topology for function lattices and realcompactness.
The space of entire functions of two variables as a metric space.
The space of Laplace transformable distributions
The space of real-analytic functions has no basis
Let Ω be an open connected subset of . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
The spaces and the symbolic calculus of Sebastião e Silva. (Les espaces et le calcul symbolique de Sebastião e Silva.)
The Theorems of F. and M. Riesz for Circular Sets.
The topological complexity of sets of convex differentiable functions.
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
The topological proof of the Nachbin-Shirota's theorem