Nonconstant locally recurrent functions

Donald Charles Benson

Vol. 21 (1967), No. 3, 437–443

DOI: 10.2140/pjm.1967.21.437

Abstract

The purpose of this paper is to develop a new method of using the Baire Category Theorem to obtain counterexamples in analysis. The method is used to show that a certain class of nonconstant locally recurrent functions is of second category in a suitable metric space of continuous functions. In §1 an explicit example is given of a nonconstant locally recurrent function. This example is included because it clarffies the category argument in §4.

Mathematical Subject Classification

Primary: 26.49

Milestones

Received: 27 May 1966

Published: 1 June 1967