Preface

Mardešić, Sibe; Segal, Jack

doi:10.1016/b978-0-444-86286-0.50005-2

Cited by 67 publications

(153 citation statements)

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“…Since K is a commutative cofinite sequence, one can provide it with meshes ek and view K also as an approximate sequence. (7) shows that the inclusion maps \(K )(n)| -<• \K \ define a map of approximate systems. The existence of fK and its properties now follow from the general theory of maps between approximate systems (see [10 or 17]).…”

Section: Cohomological Dimension Of Limits Of Approximate Systemsmentioning

confidence: 99%

“…It is well known that every compact Hausdorff space X is the limit of a (commutative) inverse system of compact polyhedra X = (Xa,paa,,A) (with PL bonding maps paa, ) (see, e.g., [7,I,§5.2,Theorem 7]). However, B.…”

Section: Representing Compact Spaces As Approximate Limitsmentioning

confidence: 99%

“…One can achieve that U = \L\ where L is a subcomplex of the j th barycentric subdivision A"a2 of Ka for some sufficiently large j. Choose n > 0 so small that (7) d(x',xai)<3n^x'G\L\, and choose k > j so large that (8) 3 mesh A¿ < n.…”

Section: The Mapping F:z->xmentioning

confidence: 99%

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Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Mardešić¹,

Rubin²

1989

Trans. Amer. Math. Soc.

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Section: Cohomological Dimension Of Limits Of Approximate Systemsmentioning

confidence: 99%

Section: Representing Compact Spaces As Approximate Limitsmentioning

confidence: 99%

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Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Mardešić¹,

Rubin²

1989

Trans. Amer. Math. Soc.

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“…Whereas functor J is faithful and fixes objects, we can consider pro-C as a subcategory of pro * -C. Now, let D be a pro-reflective and full subcategory of C, which means that every X ∈ Ob(C) admits a D-expansion (see more in [7]). Let p :…”

Section: Preliminariesmentioning

confidence: 99%

“…At this step we can introduce the (abstract) shape category Sh (C,D) and (abstract) coarse shape category Sh * (C,D) for a pair (C, D) (see more in [4] and [7]). Objects of these two categories are all objects of C and morphisms …”

Section: Preliminariesmentioning

confidence: 99%

Topological coarse shape groups of compact metric spaces

Bilan¹,

Čuka²

2017

Rad Hrvatske akademije znanosti i umjetnosti

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Abstract. The shape theory and, relatively new, coarse shape theory are very useful in studying of topological spaces, as well as of the corresponding algebraic invariants, especially, shape and coarse shape groups. By using certain ultrametrics on special sets of pro-and pro * -morphisms, we topologize those groups when they refer to compact metric spaces and we get topological groups. In the shape case, they are isomorphic to recently constructed topological shape homotopy groups, while in the coarse shape case we get the coarse shape invariants, denoted byπ * d * k (X, x 0 ). We have proven some important properties ofπ * d * k (X, x 0 ) and provided few interesting examples.

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Constrained deformations of positive scalar curvature metrics, II

Carlotto,

2023

Comm Pure Appl Math

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We prove that various spaces of constrained positive scalar curvature metrics on compact three‐manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the mean‐convex and the minimal case. We then discuss the implications of these results on the topology of different subspaces of asymptotically flat initial data sets for the Einstein field equations in general relativity.

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Preface

Cited by 67 publications

References 0 publications

Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Topological coarse shape groups of compact metric spaces

Constrained deformations of positive scalar curvature metrics, II

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