Homeomorphisms with many recurrent points
Author: Benjamin Halpern
Journal: Proc. Amer. Math. Soc. 59 (1976), 159-160
MSC: Primary 58F10; Secondary 58F20, 58D99
MathSciNet review: 0415678
Abstract: Let be a topological space and the space of all homeomorphisms of onto itself with the compact open topology. If and , then is a recurrent point of provided is in the closure of . It is shown that if is Hausdorff and is a nonempty open subset of homeomorphic to Euclidean -dimensional space with , then the recurrent points of are dense in is nowhere dense in .
Keywords: Homeomorphism, recurrent point, manifold, compact open topology
Article copyright: © Copyright 1976 American Mathematical Society