Homotopy theories and model categories
... pushouts and homotopy pullbacks in a model category. What we do along these lines can certainly be carried further. This paper is not in any sense a survey of everything that is known about model categories; in fact we cover only a fraction of the material in [22]. The last section has a discussion ...
... pushouts and homotopy pullbacks in a model category. What we do along these lines can certainly be carried further. This paper is not in any sense a survey of everything that is known about model categories; in fact we cover only a fraction of the material in [22]. The last section has a discussion ...
ON THE UPPER LOWER SUPER. D-CONTINUOUS
... (b) Every upper-lower semi continuous multifunction from ( X , r ) into a space (Y, 7) is upper-lower D-super continuous. Proof. (a)=>(b):Obvious (b)=>(a):Take (Y, 7) = ( X , 7-). Then the identity multifunction Ix on X is upper-lower semi continuous and hence upper-lower D-super continuous.Thus by ...
... (b) Every upper-lower semi continuous multifunction from ( X , r ) into a space (Y, 7) is upper-lower D-super continuous. Proof. (a)=>(b):Obvious (b)=>(a):Take (Y, 7) = ( X , 7-). Then the identity multifunction Ix on X is upper-lower semi continuous and hence upper-lower D-super continuous.Thus by ...
![arXiv:1205.2342v1 [math.GR] 10 May 2012 Homogeneous compact](http://s1.studyres.com/store/data/014455921_1-3cd5e27d3d632291f2fbeb8ac68a29b6-300x300.png)
On function field Mordell-Lang and Manin-Mumford
... This paper concerns relationships between “known” results. The original motivation was to supply a transparent account of function field Mordell-Lang in positive characteristic. After the third author gave a talk on the topic of reducing Mordell-Lang to Manin-Mumford, in Paris, December 2010, Damian ...
... This paper concerns relationships between “known” results. The original motivation was to supply a transparent account of function field Mordell-Lang in positive characteristic. After the third author gave a talk on the topic of reducing Mordell-Lang to Manin-Mumford, in Paris, December 2010, Damian ...
Convexity of Hamiltonian Manifolds
... Suppose there is a convex subset B ⊆ t+ such that ψ −1 (B) is disconnected. Then ψ −1 (B) is the disjoint union of two non-empty open subsets, say U and V . Let u ∈ ψ(U ) and v ∈ ψ(V ) . Since B is convex, we have uv ⊆ B , hence X := ψ −1 (uv) ⊆ ψ −1 (B) . Thus, X = (X ∩ U ) ∪ (X ∩ V ) is the disjoi ...
... Suppose there is a convex subset B ⊆ t+ such that ψ −1 (B) is disconnected. Then ψ −1 (B) is the disjoint union of two non-empty open subsets, say U and V . Let u ∈ ψ(U ) and v ∈ ψ(V ) . Since B is convex, we have uv ⊆ B , hence X := ψ −1 (uv) ⊆ ψ −1 (B) . Thus, X = (X ∩ U ) ∪ (X ∩ V ) is the disjoi ...
![arXiv:math/0412558v2 [math.GN] 10 Apr 2016](http://s1.studyres.com/store/data/000780140_1-7e82978ab888d179066aebd70a132571-300x300.png)
arXiv:math/0412558v2 [math.GN] 10 Apr 2016
... immediately fit into the hierarchy formed by the others that we have named (see Figure 1.1). That a first countable normal space need not be perfectly normal is well known. Furthermore, [Arens(1950)] has given an example of a perfectly normal space that is not sequential. It seems, however, that the ...
... immediately fit into the hierarchy formed by the others that we have named (see Figure 1.1). That a first countable normal space need not be perfectly normal is well known. Furthermore, [Arens(1950)] has given an example of a perfectly normal space that is not sequential. It seems, however, that the ...