Universal spaces for almost n-dimensionality

M. Abry, J.J. Dijkstra

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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 Erdös space. © 2007 American Mathematical Society Reverts to public domain 28 years from publication.
Original languageEnglish
Pages (from-to)2623-2628 (electronic)
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number8
Publication statusPublished - 2007

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