References in periodicals archive

In [1], some results about Segal algebras were obtained, where one of the conditions that had to be fulfilled was that the set [C.sub.0](X,K)[cross product]B (the full definition of this set will be given further in this paper) had to be dense in [C.sub.0](X,B) (in the compact-open topology) for a topological algebra B.

Consider the algebra ([C.sub.0](X,Y),[c.sub.Y]) of all continuous maps f : X [right arrow] Y vanishing at infinity equippped with the compact-open topology [c.sub.Y], where the subbase of the topology [c.sub.Y] on [C.sub.0](X, Y) consists of all sets of the form

About the density property in the space of continuous maps vanishing at infinity

The space C(X) endowed with the pointwise topology or with the compact-open topology is denoted by [C.sub.p](X) and [C.sub.k](X), respectively.

Free Subspaces of Free Locally Convex Spaces

Consider the algebra [C.sub.c](X) of continuous complex valued functions on X, endowed with the compact-open topology. Then [C.sub.c](X) is a unital commutative complete locally uniformly A-convex algebra.

On different barrelledness notions in locally convex algebras

O'Meara, On paracompactness in function spaces with the compact-open topology, Proc.

Notes on mssc-images of relatively compact metric spaces

When C(X) is equipped with the compact-open topology [[tau].sub.c] we write [C.sub.c](X).

A Characterization of the Existence of a Fundamental Bounded Resolution for the Space [C.sub.c] (X) in Terms of X

Let's recall the definitions: By O (X) we denote the algebra of holomorphic functions on X endowed with compact-open topology. By Stein's original definition, simplified by later developments, a complex manifold X is Stein (or, as Karl Stein put it, holomorphically complete) if it satisfies the following two conditions.

In this paper we consider the ring R = [SL.sub.n](O(X)) of holomorphic maps from a Stein space X to [SL.sub.n](C) endowed with compact-open topology, the natural topology for holomorphic mappings.

On Kazhdan's property (T) for the special linear group of holomorphic functions

For a metric space, Iso(X) denotes the group of all surjective self-isometries of X equipped with the topology of pointwise convergence, induced by the embedding Iso(X) [??] [X.sup.X] (or, which is the same, compact-open topology).

Fixed point-free isometric actions of topological groups on Banach spaces

introduced a topology on higher homotopy groups of a pointed space (X, x) as a quotient of Hom(([I.sup.n], [I.sup.n]), (X, x)) equipped with the compact-open topology and denoted it by [[pi].sup.top.sub.n] (X, x).

On nondiscreteness of a higher topological homotopy group and its cardinality