Chapter 31 (Compact-Open topology)

olivierd

Aug 1, 2017 2 min read

Margin between a compact subspace and an including open subspace

In Chapter 31 (“Compact-Open Topology”), the fact that, on the set of the continuous mappings the second topology (the uniform convergence topology) is finer than the first (the compact-open topology) is said to be “clear” but actually needs some non-trivial proof. Part of this is the lemma that I state and prove below. For any …

Uniform convergence topology and the open set topology

Chapter 31, “The Compact-Open Topology”, describes the compact-open topology, and goes on to compare it with two other topologies on in the case where . It asserts that “clearly” the second of these three is finer than the first, and the third finer than the second. This may well be “clear” intuitively, but is not…

Category: Chapter 31 (Compact-Open topology)

Margin between a compact subspace and an including open subspace

Uniform convergence topology and the open set topology