Continuity in separable metrizable and Lindelöf spaces

Authors:
Chris Good and Sina Greenwood

Journal:
Proc. Amer. Math. Soc. **138** (2010), 577-591

MSC (2000):
Primary 37B99, 54A10, 54B99, 54C05, 54D20, 54D65, 54H20; Secondary 37-XX

DOI:
https://doi.org/10.1090/S0002-9939-09-10149-1

Published electronically:
October 14, 2009

MathSciNet review:
2557175

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-09-10149-1

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.