Fenestrations induced by perfect tilings

F.G. Arenas, M.L. Puertas

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.


Keywords

Fenestration; Tiling; Grid; Trace spaces; Lower semicontinuous decomposition

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References

F.G. Arenas, Tilings in topological spaces, Int. J. Math. Math. Sci. 22 (1999), No.3, 611-616.

B. Grunbaum and G.C. Shephard, Tilings and Patterns, Freeman, New York, 1986.

E.H. Kronheimer, The topology of digital images, Topology Appl. , 46 (1992), 279-303. http://dx.doi.org/10.1016/0166-8641(92)90019-V

Mark J. Nielsen, Singular points of a convex tiling, Math. Ann. 284 (1989), 601-616. http://dx.doi.org/10.1007/BF01443354

Mark J. Nielsen, Singular points of a star-finite tiling, Geom. Dedic. 33 (1990), 99-109. http://dx.doi.org/10.1007/BF00147605

Mark J. Nielsen, On two questions concerning tilings, Israel J. Math. 81 (1993), 129-143. http://dx.doi.org/10.1007/BF02761301

Stephen Willard, General Topology, Addison-Wesley Publ. Comp. 1970.

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Universitat Politècnica de València

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