spaces of holomorphic functions and their duality
... and only if for each p ∈ S, supx∈B p(x) < ∞. Hence in H(G), a set is bounded if and only if it is uniformly bounded on compact subsets of G. In a general locally convex space, each compact set is clearly bounded. A crucial property of H(G) is that the converse holds: Definition 14 A subset of H(U) i ...
... and only if for each p ∈ S, supx∈B p(x) < ∞. Hence in H(G), a set is bounded if and only if it is uniformly bounded on compact subsets of G. In a general locally convex space, each compact set is clearly bounded. A crucial property of H(G) is that the converse holds: Definition 14 A subset of H(U) i ...
Section 6: Manifolds There are lots of different topological spaces
... There are lots of different topological spaces, some of which are very strange, counter-intuitive, and pathological, but also interesting. Some topological spaces, on the other hand, are in some sense very “nice and intuitive.” We are going to focus our studies on the latter kind: manifolds. These a ...
... There are lots of different topological spaces, some of which are very strange, counter-intuitive, and pathological, but also interesting. Some topological spaces, on the other hand, are in some sense very “nice and intuitive.” We are going to focus our studies on the latter kind: manifolds. These a ...
co-γ-Compact Generalized Topologies and c
... was introduced by Gentry and Hoyle [8]. Let (X, τ1 ) and (Y, τ2 ) be topological spaces. A function f : (X, τ1 ) −→ (Y, τ2 ) is defined to be c-continuous if for each point x ∈ X and each open set V in Y containing f (x) and having compact complement, there exists an open set U in X containing x such ...
... was introduced by Gentry and Hoyle [8]. Let (X, τ1 ) and (Y, τ2 ) be topological spaces. A function f : (X, τ1 ) −→ (Y, τ2 ) is defined to be c-continuous if for each point x ∈ X and each open set V in Y containing f (x) and having compact complement, there exists an open set U in X containing x such ...
