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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universal spaces for almost $ n$-dimensionality


Authors: Mohammad Abry and Jan J. Dijkstra
Journal: Proc. Amer. Math. Soc. 135 (2007), 2623-2628
MSC (2000): Primary 54F45, 54C25
Published electronically: March 22, 2007
MathSciNet review: 2302584
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Abstract: We find universal functions for the class of lower semi-continuous (LSC) functions with at most $ n$-dimensional domain. In an earlier paper we proved that a space is almost $ n$-dimensional if and only if it is homeomorphic to the graph of an LSC function with an at most $ n$-dimensional domain. We conclude that the class of almost $ n$-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: http://dx.doi.org/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
Published electronically: March 22, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.