New York Journal of Mathematics
Volume 15 (2009) 245-264


Michael Barr, John F. Kennison, and R. Raphael

Local extension of maps

Published: June 2, 2009
Keywords: Extending real-valued functions
Subject: 18A20, 54C45, 54B30

We continue our investigations into absolute CR-epic spaces. Given a continuous function f:X→ Y, with X absolute CR-epic, we search for conditions which imply that Y is also absolute CR-epic. We are particularly interested in the cases when X is a dense subset of Y and when f is a quotient mapping. To answer these questions, we consider issues of local extension of continuous functions. The results on this question are of independent interest.


The first and third authors would like to thank NSERC of Canada for its support of this research. We would all like to thank McGill and Concordia Universities for partial support of the middle author's visits to Montreal.

Author information

Michael Barr:
Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 2K6

John F. Kennison:
Department of Mathematics and Computer Science, Clark University, Worcester, MA 01610

R. Raphael:
Department of Mathematics and Statistics, Concordia University, Montreal, QC, H4B 1R6