Fenestrations induced by perfect tilings
Submitted: 2014-01-27
|Accepted: 2014-01-27
|Published: 2002-04-01
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Keywords:
Fenestration, Tiling, Grid, Trace spaces, Lower semicontinuous decomposition
Supporting agencies:
Grant BFM 2000-1111 from Spanish Ministry of Science and Technology
Abstract:
In this paper we study those regular fenestrations (as defined by Kronheimer in [3]) that are obtained from a tiling of a topological space. Under weak conditions we obtain that the canonical grid is also the minimal grid associated to each tiling and we prove that it is a T0-Alexandroff
semirregular trace space. We also present some examples illustrating how the properties of the grid depend on the properties of the tiling and we pose some questions. Finally we study the topological properties of the grid depending on the properties of the space and the tiling.
References:
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