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Universal spaces for almost  -dimensionality
Author(s):
Mohammad
Abry;
Jan
J.
Dijkstra
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2623-2628.
MSC (2000):
Primary 54F45, 54C25
Posted:
March 22, 2007
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Abstract:
We find universal functions for the class of lower semi-continuous (LSC) functions with at most  -dimensional domain. In an earlier paper we proved that a space is almost  -dimensional if and only if it is homeomorphic to the graph of an LSC function with an at most  -dimensional domain. We conclude that the class of almost  -dimensional spaces contains universal elements (that are topologically complete). These universal spaces can be thought of as higher-dimensional analogues of complete Erdos space.
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Additional Information:
Mohammad
Abry
Affiliation:
Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081${}^a$, 1081 HV Amsterdam, The Netherlands
Email:
mabry@cs.vu.nl
Jan
J.
Dijkstra
Affiliation:
Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081${}^a$, 1081 HV Amsterdam, The Netherlands
Email:
dijkstra@cs.vu.nl
DOI:
10.1090/S0002-9939-07-08971-X
PII:
S 0002-9939(07)08971-X
Keywords:
Lower semi-continuous function,
universal space,
almost $ n$-dimensional space.
Received by editor(s):
November 12, 2005
Posted:
March 22, 2007
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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