Continuity in separable metrizable and Lindelöf spaces
Authors:
Chris Good and Sina Greenwood
Journal:
Proc. Amer. Math. Soc. 138 (2010), 577591
MSC (2000):
Primary 37B99, 54A10, 54B99, 54C05, 54D20, 54D65, 54H20; Secondary 37XX
Published electronically:
October 14, 2009
MathSciNet review:
2557175
Fulltext PDF Free Access
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Abstract: Given a map on a set we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on with respect to which is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of is no greater than , the cardinality of the continuum. We go on to prove that there is a Lindelöf topology on with respect to which is continuous if either or for some , where and for any ordinal and limit ordinal .
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Additional Information
Chris Good
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom
Email:
c.good@bham.ac.uk
Sina Greenwood
Affiliation:
University of Auckland, Private Bag 92019, Auckland, New Zealand
Email:
sina@math.auckland.ac.nz
DOI:
http://dx.doi.org/10.1090/S0002993909101491
Keywords:
Abstract dynamical system,
topological dynamical system,
Lindel\"of,
separable metric,
hereditarily Lindel\"of
Received by editor(s):
October 1, 2008
Published electronically:
October 14, 2009
Communicated by:
Jane M. Hawkins
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
