![arXiv:1311.6308v2 [math.AG] 27 May 2016](http://s1.studyres.com/store/data/014155230_1-8dc9a9d84bdbfdfdd374aa0278f9f3e1-300x300.png)
Topology Proceedings - topo.auburn.edu
... Lemma 3.1 ([4]). Let X be a GO-space. Then X is hereditarily paracompact iff X − {x} is paracompact for each point x ∈ X. Lemma 3.2. Let X, Y be GO-spaces. If Y has both a left and a right endpoint, and (1) if A is discrete in X and B is discrete in Y , then A ∗ B is discrete in the GOTP(X ∗ Y ); (2 ...
... Lemma 3.1 ([4]). Let X be a GO-space. Then X is hereditarily paracompact iff X − {x} is paracompact for each point x ∈ X. Lemma 3.2. Let X, Y be GO-spaces. If Y has both a left and a right endpoint, and (1) if A is discrete in X and B is discrete in Y , then A ∗ B is discrete in the GOTP(X ∗ Y ); (2 ...
Galois Extensions of Structured Ring Spectra
... In other words, for a faithful E-local G-Galois extension A → B with B connected there is a bijective contravariant Galois correspondence K ↔ C = B hK between the subgroups of G and the weak equivalence classes of separable A-algebras mapping faithfully to B. The inverse correspondence takes C to K ...
... In other words, for a faithful E-local G-Galois extension A → B with B connected there is a bijective contravariant Galois correspondence K ↔ C = B hK between the subgroups of G and the weak equivalence classes of separable A-algebras mapping faithfully to B. The inverse correspondence takes C to K ...
Abstract Simplicial Complexes
... Summary. In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties. ...
... Summary. In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties. ...
Lecture Notes on Smale Spaces
... Next, we turn to the definition of irreducibility. Definition 1.1.4. Let X be a topological space and let f be a homeomorphism of X. We say the system (X, f ) is irreducible if, for every (ordered) pair of non-empty open sets, U, V , there is a positive integer n such that f n (U ) ∩ V is non-empty. ...
... Next, we turn to the definition of irreducibility. Definition 1.1.4. Let X be a topological space and let f be a homeomorphism of X. We say the system (X, f ) is irreducible if, for every (ordered) pair of non-empty open sets, U, V , there is a positive integer n such that f n (U ) ∩ V is non-empty. ...
rings of real-valued continuous functions. i
... set {tt«}".! of functions in S(X, R) which are positive everywhere. We shall show that there exists a neighborhood IL¿(0) in (S(X, R) which contains no neighborhood U»-„(0). Let bn = 2-lmm [vi(pn), ir2(pn), ■ • ■ , irn(pn)], for n = \, 2, 3, ■ ■ ■ . There obviously exists a function a in S(i?, R) su ...
... set {tt«}".! of functions in S(X, R) which are positive everywhere. We shall show that there exists a neighborhood IL¿(0) in (S(X, R) which contains no neighborhood U»-„(0). Let bn = 2-lmm [vi(pn), ir2(pn), ■ • ■ , irn(pn)], for n = \, 2, 3, ■ ■ ■ . There obviously exists a function a in S(i?, R) su ...
