Closed subsets of a CAT(0) 2–complex are intrinsically CAT(0)
نویسندگان
چکیده
Let k be at most 0, and let X a locally-finite CAT(k) polyhedral 2-complex X, each face with constant curvature k. E closed, rectifiably-connected subset of trivial first singular homology. We show that E, under the induced path metric, is complete space.
منابع مشابه
Spaces Whose Pseudocompact Subspaces Are Closed Subsets
Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some exam...
متن کاملSOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS
Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...
متن کاملAn Instructional Environment for Practicing Argumentation Skills
CAT0 is an instructions environment for practicing basic skills of legal research: to use cases in arguments about a problem situation and to test a theory about a legal domain. Using the CAT0 tools, law students analyze a legal problem, frame queries of CATO’S database of legal cases, and judge how relevant the retrieved cases are to their developing argument or theory. CAT0 aids hming by maki...
متن کاملIntervals in Lattices of -Meet-Closed Subsets
We study abstract properties of intervals in the complete lattice of all meet-closed subsets ( -subsemilattices) of a -(meet-)semilattice S, where is an arbitrary cardinal number. Any interval of that kind is an extremally detachable closure system (that is, for each closed set A and each point x outside A, deleting x from the closed set generated by A and x leaves a closed set). Such closure s...
متن کاملForcing closed unbounded subsets of א
1. Introduction Suppressing some important technical hypotheses for the moment, the project under-taken in this paper is this: Given a tree T of height and cardinality ω 1 , construct (uniformly in T) a subset S T ⊆ ℵ ω 1 +1 such that, if W is an outer model of V having the same ω 1 , ℵ ω 1 , and ℵ ω 1 +1 in which S T has a closed unbounded (club) subset, then T has a cofinal branch in W. Conve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2021
ISSN: ['1472-2739', '1472-2747']
DOI: https://doi.org/10.2140/agt.2021.21.1723