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Tiling Spaces Are Inverse Limits
Let M be an arbitrary Riemannian homogeneous space, and let Ω be a space of tilings of M , with finite local complexity (relative to some symmetry group Γ) and closed in the natural topology. Then Ω is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Γ. This ...
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We continue the investigation of CW homotopy type of spaces of continuous functions between two CW complexes begun by J. Milnor in 1959 and P. Kahn in 1984. Viewing function spaces as particular cases of inverse limits we also study certain inverse systems of fibrations between CW homotopy type spaces. If the limit space Z∞ of an inverse sequence {Zi} of fibrations between CW type spaces has CW...
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THEOREM I. Let X be a small category. Then the following assertions are equivalent: (1) The inverse limit proj limx: AB-^AB is exact (2) For every abelian category SÏ with exact direct products y the inverse limit proj lim* : %—»3I is exact. (3) Every connected component Y of X contains an object y together with an endomorphism eÇz Y (y, y) such that the following properties are satisfied: (i) ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0220240-6