Universal spaces for almost $n$-dimensionality
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- by Mohammad Abry and Jan J. Dijkstra PDF
- Proc. Amer. Math. Soc. 135 (2007), 2623-2628 Request permission
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 Erdős space.References
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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
- MR Author ID: 58030
- Email: dijkstra@cs.vu.nl
- Received by editor(s): November 12, 2005
- Published electronically: March 22, 2007
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2623-2628
- MSC (2000): Primary 54F45, 54C25
- DOI: https://doi.org/10.1090/S0002-9939-07-08971-X
- MathSciNet review: 2302584