Locally Compact Path Spaces

It is shown that the space X[0,1], of continuous maps [0, 1] X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T1-space X, it follows that X[0,1] is locally compact if and only if X is locally compact and totally path-disconnected. AMS Classification: 54C35, 54E45, 55P35, 18B30, 18D15 Key Words: locally compact, compact-open topology, path space

• Type: Journal
• Year: 2005
• Where: ACS
• Authors: Susan B. Niefield
• Keywords: ACS 2005, ACS 2007, Compact-open Topology, Locally Compact, Space X