Group structures of a function spaces with the set-open topology

Abstract

In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and other algebraic structures) under the usual operations of addition and multiplication (and multiplication by scalars).

9 pages

References in corpus (1)

• Uniformity of uniform convergence on the family of sets

Cited by in corpus (1)

• On homeomorphism groups and the set-open topology