KukielaAlex.pdf
... take roughly the same route, but avoid falling into the same trap. In Sections 2 and 3 we prepare the ground for further results. Basic facts concerning Alexandroff spaces are recalled and the classes of locally finite spaces, fp-spaces and bp-spaces are introduced. Section 4 is a study of the compa ...
... take roughly the same route, but avoid falling into the same trap. In Sections 2 and 3 we prepare the ground for further results. Basic facts concerning Alexandroff spaces are recalled and the classes of locally finite spaces, fp-spaces and bp-spaces are introduced. Section 4 is a study of the compa ...
On a fuzzy topological structure
... let (X, f ) denote their product. Take u € I a for every a and let y«€lX denote the product of all Ma ( i.e. /((x) = A Aa(xa) where xe X and x a denotes the a-est coordinate). Quite similarly as above one can show that T K (/c) > ^t^fta) *and hence ^ e degree of closedness of the product of fulzy se ...
... let (X, f ) denote their product. Take u € I a for every a and let y«€lX denote the product of all Ma ( i.e. /((x) = A Aa(xa) where xe X and x a denotes the a-est coordinate). Quite similarly as above one can show that T K (/c) > ^t^fta) *and hence ^ e degree of closedness of the product of fulzy se ...
pdf
... sse groupoids, understood in the sense defined above, and all functors are smooth, i.e. they are given by smooth maps on the spaces of objects and morphisms.3 Many authors call ep groupoids orbifold groupoids. Note that stability4 is a consequence of properness, but we shall often assume the former ...
... sse groupoids, understood in the sense defined above, and all functors are smooth, i.e. they are given by smooth maps on the spaces of objects and morphisms.3 Many authors call ep groupoids orbifold groupoids. Note that stability4 is a consequence of properness, but we shall often assume the former ...
1 Well-ordered sets 2 Ordinals
... such that each map Xβ → Xβ+1 is in D , the map of sets colimβ<λ C (A, Xβ ) → C (A, colimβ<λ Xβ ) is an isomorphism. We say that A is small relative to D if it is κ-small for some κ. We say that A is small if it is small relative to the whole category C . We say that A is finite relative to D if it i ...
... such that each map Xβ → Xβ+1 is in D , the map of sets colimβ<λ C (A, Xβ ) → C (A, colimβ<λ Xβ ) is an isomorphism. We say that A is small relative to D if it is κ-small for some κ. We say that A is small if it is small relative to the whole category C . We say that A is finite relative to D if it i ...
from mapping class groups to automorphism groups of free groups
... it is a CW-pair, so we get a homotopy h : (X × I) × I → X from H to a homotopy H : X × I → X with H (X × 0) = f (X), H (X × 1) = g(X) and H (∂X × I) is the constant map on ∂X. Hence f and g are homotopic relative to ∂X. By a ∆-category, we mean a category enriched over simplicial sets. Let T ...
... it is a CW-pair, so we get a homotopy h : (X × I) × I → X from H to a homotopy H : X × I → X with H (X × 0) = f (X), H (X × 1) = g(X) and H (∂X × I) is the constant map on ∂X. Hence f and g are homotopic relative to ∂X. By a ∆-category, we mean a category enriched over simplicial sets. Let T ...
... Proof: (i) Let A be a (i,j) gr*-closed subset of (X,1,2). Let U GO(X,i) be such that A U. Then by hypothesis j-rcl(A) U. This implies j-cl(A) U. Therefore A is (i,j) gr*-closed. Proof of (ii) to (v) are similar to (i). The following examples show that the reverse implications of above p ...
Embeddings from the point of view of immersion theory : Part I
... Recently Goodwillie [9], [10], [11] and Goodwillie–Klein [12] proved higher excision theorems of Blakers–Massey type for spaces of smooth embeddings. In conjunction with a calculus framework, these lead to a calculation of such spaces when the codimension is at least 3. Here the goal is to set up th ...
... Recently Goodwillie [9], [10], [11] and Goodwillie–Klein [12] proved higher excision theorems of Blakers–Massey type for spaces of smooth embeddings. In conjunction with a calculus framework, these lead to a calculation of such spaces when the codimension is at least 3. Here the goal is to set up th ...
algebraic geometry and the generalisation of bezout`s theorem
... things from a point of view which rendered a difficult problem much clearer. This was a great help when trying to wade through a host of well written but at times very complicated texts on the subject. Secondly, I thank the University of New South Wales and in particular the School of Mathematics fo ...
... things from a point of view which rendered a difficult problem much clearer. This was a great help when trying to wade through a host of well written but at times very complicated texts on the subject. Secondly, I thank the University of New South Wales and in particular the School of Mathematics fo ...
Manifolds and Topology MAT3024 2011/2012 Prof. H. Bruin
... An equivalence relation ∼ on a space X is a relation on a set which is 1. Reflexive: x ∼ x. 2. Symmetric: x ∼ y if and only if y ∼ x. 3. Transitive: x ∼ y and y ∼ z imply x ∼ z. The set {y ∈ X : y ∼ x} is the equivalence class of x; it is denoted as [x]. Definition 20 Given an equivalence relation ∼ ...
... An equivalence relation ∼ on a space X is a relation on a set which is 1. Reflexive: x ∼ x. 2. Symmetric: x ∼ y if and only if y ∼ x. 3. Transitive: x ∼ y and y ∼ z imply x ∼ z. The set {y ∈ X : y ∼ x} is the equivalence class of x; it is denoted as [x]. Definition 20 Given an equivalence relation ∼ ...