The local structure of algebraic K-theory
... Figure 2: The differential of K and T C is equal at any point. For rings it is the homology of the category of finitely generated projective modules ...
... Figure 2: The differential of K and T C is equal at any point. For rings it is the homology of the category of finitely generated projective modules ...
Algebraic Topology
... To avoid overusing the word ‘continuous’ we adopt the convention that maps between spaces are always assumed to be continuous unless otherwise stated. ...
... To avoid overusing the word ‘continuous’ we adopt the convention that maps between spaces are always assumed to be continuous unless otherwise stated. ...
Intuitionistic Fuzzy Metric Groups - International Journal of Fuzzy
... well-known fixed point theorems of Banach and Edelstein to fuzzy metric spaces. The notion of fuzzy metric space plays a fundamental role in fuzzy topology, so many authors have studied several notions of fuzzy metric. Somewhat reformulating the Kramosil and Michalek’ s definition, George and Veeram ...
... well-known fixed point theorems of Banach and Edelstein to fuzzy metric spaces. The notion of fuzzy metric space plays a fundamental role in fuzzy topology, so many authors have studied several notions of fuzzy metric. Somewhat reformulating the Kramosil and Michalek’ s definition, George and Veeram ...
Topolog´ıa Algebraica de Espacios Topológicos Finitos y Aplicaciones
... the theory of finite spaces and to investigate their applications to the homotopy theory and simple homotopy theory of polyhedra and general topological spaces. We use, in particular, some of the results that we obtain, to analize two important open conjectures of algebraic and geometric topology: Q ...
... the theory of finite spaces and to investigate their applications to the homotopy theory and simple homotopy theory of polyhedra and general topological spaces. We use, in particular, some of the results that we obtain, to analize two important open conjectures of algebraic and geometric topology: Q ...
barmakthesis.pdf
... it seems that he was unaware of Stong’s and McCord’s results on finite spaces. We will see that the finite space point of view adds a completely new dimension to his conjecture and allows to attack the problem with new topological and combinatorial tools. We will show that Whitehead’s Theorem does ...
... it seems that he was unaware of Stong’s and McCord’s results on finite spaces. We will see that the finite space point of view adds a completely new dimension to his conjecture and allows to attack the problem with new topological and combinatorial tools. We will show that Whitehead’s Theorem does ...
Introduction to Topological Groups
... theorem. The first one is a description of the precompact group topologies of the abelian groups (§10.1). The main application of Følner’s theorem is an immediate proof of Peter-Weyl’s theorem (in §10.3). §10.4 is dedicated to the almost periodic functions of the abelian group. As another applicatio ...
... theorem. The first one is a description of the precompact group topologies of the abelian groups (§10.1). The main application of Følner’s theorem is an immediate proof of Peter-Weyl’s theorem (in §10.3). §10.4 is dedicated to the almost periodic functions of the abelian group. As another applicatio ...
Metric geometry of locally compact groups
... – And the tightly interwoven developments of combinatorial group theory and low dimensional topology, from Dehn to Thurston, and so many others. From 1980 onwards, for all these reasons and under guidance of Gromov, in particular of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group commu ...
... – And the tightly interwoven developments of combinatorial group theory and low dimensional topology, from Dehn to Thurston, and so many others. From 1980 onwards, for all these reasons and under guidance of Gromov, in particular of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group commu ...
On Chains in H-Closed Topological Pospaces
... and ↓a are closed subsets of X for each a ∈ X. A topological space equipped with a continuous partial order is called a topological partially ordered space or shortly topological pospace. A partial order on a topological space X is continuous if and only if the graph of is a closed subset in X × ...
... and ↓a are closed subsets of X for each a ∈ X. A topological space equipped with a continuous partial order is called a topological partially ordered space or shortly topological pospace. A partial order on a topological space X is continuous if and only if the graph of is a closed subset in X × ...
MONODROMY AND FAITHFUL REPRESENTABILITY OF LIE
... A topological groupoid is a groupoid G , together with a topology on the set G1 and a topology on the set G0 such that all the structure maps are continuous. With continuous functors as homomorphisms, topological groupoids form a category Gpd. To make the terminology precise, we will say that a C ∞ ...
... A topological groupoid is a groupoid G , together with a topology on the set G1 and a topology on the set G0 such that all the structure maps are continuous. With continuous functors as homomorphisms, topological groupoids form a category Gpd. To make the terminology precise, we will say that a C ∞ ...
Surveys on Surgery Theory : Volume 1 Papers dedicated to C. T. C.
... The importance of this notion stems from the h-cobordism theorem of Smale (ca. 1960), which showed that if M and N are simply connected and of dimension ≥ 5, then every h-cobordism between M and N is a cylinder M × I. The crux of the proof involves handle cancellations as well as Whitney’s trick for ...
... The importance of this notion stems from the h-cobordism theorem of Smale (ca. 1960), which showed that if M and N are simply connected and of dimension ≥ 5, then every h-cobordism between M and N is a cylinder M × I. The crux of the proof involves handle cancellations as well as Whitney’s trick for ...
THE HOMOMORPHISMS OF TOPOLOGICAL GROUPOIDS 1
... The main purpose of this paper is to study topological groupoid homomorphisms and to give some kinds of special topological groupoid homomorphisms. Finally, some characterizations of these homomorphisms are given. AMS Mathematics Subject Classification (2010): 22A22, 20L05 Key words and phrases: Top ...
... The main purpose of this paper is to study topological groupoid homomorphisms and to give some kinds of special topological groupoid homomorphisms. Finally, some characterizations of these homomorphisms are given. AMS Mathematics Subject Classification (2010): 22A22, 20L05 Key words and phrases: Top ...
Metric geometry of locally compact groups
... setting, we distinguish four classes, each class properly containing the next one: (all) all discrete groups; (ct) countable groups; (fg) finitely generated groups; (fp) finitely presented groups. This will serve as a guideline below, in the more general setting of locally compact groups. Every grou ...
... setting, we distinguish four classes, each class properly containing the next one: (all) all discrete groups; (ct) countable groups; (fg) finitely generated groups; (fp) finitely presented groups. This will serve as a guideline below, in the more general setting of locally compact groups. Every grou ...
Projective Geometry on Manifolds - UMD MATH
... The development of synthetic projective geometry was begun by the architect Desargues in 1636–1639 out of attempts to understand the geometry of perspective. Two hundred years later non-Euclidean (hyperbolic) geometry was developed independently and practically simultaneously by Bolyai in 1833 and L ...
... The development of synthetic projective geometry was begun by the architect Desargues in 1636–1639 out of attempts to understand the geometry of perspective. Two hundred years later non-Euclidean (hyperbolic) geometry was developed independently and practically simultaneously by Bolyai in 1833 and L ...
Locally normal subgroups of totally disconnected groups. Part II
... said to be h.j.i. if every non-trivial closed locally normal subgroup is open. • atomic type: |LN (G)| > 2 but LC(G) = {0, ∞}, there is a unique least element of LN (G) r {0}, the action of G on LN (G) is trivial and G is not abstractly simple. • non-principal filter type (abbreviated by NPF type): ...
... said to be h.j.i. if every non-trivial closed locally normal subgroup is open. • atomic type: |LN (G)| > 2 but LC(G) = {0, ∞}, there is a unique least element of LN (G) r {0}, the action of G on LN (G) is trivial and G is not abstractly simple. • non-principal filter type (abbreviated by NPF type): ...
Introduction to Topological Manifolds (Second edition)
... the proofs here are phrased in such a way that they will apply verbatim to the more general theorems about covering spaces in Chapter 11. Chapter 9 is a brief digression into group theory. Although a basic acquaintance with group theory is an essential prerequisite, most undergraduate algebra course ...
... the proofs here are phrased in such a way that they will apply verbatim to the more general theorems about covering spaces in Chapter 11. Chapter 9 is a brief digression into group theory. Although a basic acquaintance with group theory is an essential prerequisite, most undergraduate algebra course ...
Lectures on Groups of Transformations
... Definition. Let G be a transformation group of a space X. A slice A at a point x ∈ X is a slice such that (i)x ∈ A, (ii) G(A|A) = G(x). Note that a slice need not be a slice at any of its points. Definition . Let G be a transformation group of a space X. A normal slice is a slice A such that G(y) = ...
... Definition. Let G be a transformation group of a space X. A slice A at a point x ∈ X is a slice such that (i)x ∈ A, (ii) G(A|A) = G(x). Note that a slice need not be a slice at any of its points. Definition . Let G be a transformation group of a space X. A normal slice is a slice A such that G(y) = ...
Universitat Jaume I Departament de Matem` atiques BOUNDED SETS IN TOPOLOGICAL
... I would also like to thank all the members of the Mathematics Department of Jaume I University, especially in the area of mathematical analysis. It is impossible to name all of these people one by one, not only the professors, but also those whose small ordinary gestures and simple words have helped ...
... I would also like to thank all the members of the Mathematics Department of Jaume I University, especially in the area of mathematical analysis. It is impossible to name all of these people one by one, not only the professors, but also those whose small ordinary gestures and simple words have helped ...
“Research Note” TOPOLOGICAL RING
... A topological groupoid is a groupoid R such that the sets R and R0 are topological spaces, and source, target, object, inverse and composition maps are continuous. Let R and H be two topological groupoids. A morphism of topological groupoids is a pair of maps f:H→R and f0:H0→R0 such that f and f0 ar ...
... A topological groupoid is a groupoid R such that the sets R and R0 are topological spaces, and source, target, object, inverse and composition maps are continuous. Let R and H be two topological groupoids. A morphism of topological groupoids is a pair of maps f:H→R and f0:H0→R0 such that f and f0 ar ...
on the ubiquity of simplicial objects
... where for any y ∈ K1 we have d0 y ∼ d1 y. We call π0 (K) the set of path-connected components of K, and K is said to be path-connected if π0 (K) contains only a single element. Proposition 2.2.1. Let (K, k0 ) be a Kan pair. Then πn (K, k0 ) is a group for n ≥ 1. Proof. Take α, β ∈ πn (K, k0 ). We de ...
... where for any y ∈ K1 we have d0 y ∼ d1 y. We call π0 (K) the set of path-connected components of K, and K is said to be path-connected if π0 (K) contains only a single element. Proposition 2.2.1. Let (K, k0 ) be a Kan pair. Then πn (K, k0 ) is a group for n ≥ 1. Proof. Take α, β ∈ πn (K, k0 ). We de ...
Posets and homotopy
... simplices – finite chains in P . K : Poset → SimpComp is a functor. The homotopy type of the geometric realization of K(P ) is often called the homotopy type of P . This notion has been studied by many authors: Björner, Welker, Wachs, . . .. And it has numerous applications: ...
... simplices – finite chains in P . K : Poset → SimpComp is a functor. The homotopy type of the geometric realization of K(P ) is often called the homotopy type of P . This notion has been studied by many authors: Björner, Welker, Wachs, . . .. And it has numerous applications: ...
1 COMPACTIFICATIONS OF FRACTAL STRUCTURES 1
... addition d satisfies the condition (iii) d(x, y) = 0 iff x = y, then d is called a quasimetric. A non-archimedean quasipseudometric is a quasipseudometric that verifies d(x, y) ≤ max {d(x, z), d(z, y)} for all x, y, z ∈ X. Each quasipseudometric d on X generates a quasiuniformity Ud on X which has a ...
... addition d satisfies the condition (iii) d(x, y) = 0 iff x = y, then d is called a quasimetric. A non-archimedean quasipseudometric is a quasipseudometric that verifies d(x, y) ≤ max {d(x, z), d(z, y)} for all x, y, z ∈ X. Each quasipseudometric d on X generates a quasiuniformity Ud on X which has a ...
1. Introduction 1 2. Simplicial and Singular Intersection Homology 2
... We now define singular intersection homology as the homology of the complex whose chains are a suitable subset of the standard singular homology chains. Fix a perversity p. Definition 2.5. A singular i-simplex σ : ∆i → X is said to be p-allowable, if σ −1 (Xm−k ) ⊆ (i − k + p(k)) − skeleton of∆i . S ...
... We now define singular intersection homology as the homology of the complex whose chains are a suitable subset of the standard singular homology chains. Fix a perversity p. Definition 2.5. A singular i-simplex σ : ∆i → X is said to be p-allowable, if σ −1 (Xm−k ) ⊆ (i − k + p(k)) − skeleton of∆i . S ...
Smooth Manifolds
... This book is about smooth manifolds. In the simplest terms, these are spaces that locally look like some Euclidean space Rn , and on which one can do calculus. The most familiar examples, aside from Euclidean spaces themselves, are smooth plane curves such as circles and parabolas, and smooth surfac ...
... This book is about smooth manifolds. In the simplest terms, these are spaces that locally look like some Euclidean space Rn , and on which one can do calculus. The most familiar examples, aside from Euclidean spaces themselves, are smooth plane curves such as circles and parabolas, and smooth surfac ...
hohology of cell complexes george e. cooke and ross l. finney
... We a lso rem ar k t hat cohomology groups, which ws de f i ne for a regular complex in Chapter II, are only to uched on ...
... We a lso rem ar k t hat cohomology groups, which ws de f i ne for a regular complex in Chapter II, are only to uched on ...