NON-HAUSDORFF GROUPOIDS, PROPER ACTIONS AND K
... c : G(0) → R+ is a “cutoff” function (Section 6). Contrary to the Hausdorff case, the function c is not continuous, but it is the restriction to G(0) of a continuous map X 0 → R+ (see above for the definition of X 0 ). The Hilbert module E(G) is one of the ingredients in the definition of the assemb ...
... c : G(0) → R+ is a “cutoff” function (Section 6). Contrary to the Hausdorff case, the function c is not continuous, but it is the restriction to G(0) of a continuous map X 0 → R+ (see above for the definition of X 0 ). The Hilbert module E(G) is one of the ingredients in the definition of the assemb ...
Andr´e-Quillen (co)Homology, Abelianization and Stabilization
... Definition: Quillen Homology is the total left derived functor of abelianization. For B ∈ C, LAb(B) gives the Quillen Homology of B. Examples: C = sSets Ab(X ) = Z[X ] =⇒ LAb(X ) = Z[X ] since X is cofibrant. π∗ LAb(X ) H∗ (X ) usual homology C = T op Ab(X ) = Sp ∞ (X ) =⇒ LAb(X ) = Sp ∞ (cX ). π∗ ...
... Definition: Quillen Homology is the total left derived functor of abelianization. For B ∈ C, LAb(B) gives the Quillen Homology of B. Examples: C = sSets Ab(X ) = Z[X ] =⇒ LAb(X ) = Z[X ] since X is cofibrant. π∗ LAb(X ) H∗ (X ) usual homology C = T op Ab(X ) = Sp ∞ (X ) =⇒ LAb(X ) = Sp ∞ (cX ). π∗ ...
Proper Morphisms, Completions, and the Grothendieck Existence
... theory of quasi-finite morphisms between spectral Deligne-Mumford stacks. In particular, we will prove the following version of Zariski’s Main Theorem: if f : X → Y is quasi-compact, strongly separated, and locally quasi-finite, then f is quasi-affine (Theorem 1.2.1). In §1.3, we introduce the notio ...
... theory of quasi-finite morphisms between spectral Deligne-Mumford stacks. In particular, we will prove the following version of Zariski’s Main Theorem: if f : X → Y is quasi-compact, strongly separated, and locally quasi-finite, then f is quasi-affine (Theorem 1.2.1). In §1.3, we introduce the notio ...
Topological Dynamics: Minimality, Entropy and Chaos.
... A set B ⊆ X is said to be a redundant open set for a map f : X → Y if B is opene and f (B) ⊆ f (X \ B) (i.e., its removal from the domain of f does not change the image of f ). By taking B = X \ A one can have the following equivalent definition – a continuous map f : X → Y between topological space ...
... A set B ⊆ X is said to be a redundant open set for a map f : X → Y if B is opene and f (B) ⊆ f (X \ B) (i.e., its removal from the domain of f does not change the image of f ). By taking B = X \ A one can have the following equivalent definition – a continuous map f : X → Y between topological space ...
Motivic Homotopy Theory
... categorical point of view, the category Sch/k is intractable since it does not contain all colimits. A good (universal) way to solve this problem is by fully faithfully embedding it by the Yoneda embedding, into its category of presheaves. That is, embedding it in the category of functors Sch/k op G ...
... categorical point of view, the category Sch/k is intractable since it does not contain all colimits. A good (universal) way to solve this problem is by fully faithfully embedding it by the Yoneda embedding, into its category of presheaves. That is, embedding it in the category of functors Sch/k op G ...
Decomposition of Generalized Closed Sets in Supra Topological
... generalized locally closed sets and discuss some of their properties. 3.1 Definition Let (X, µ) be a supra topological space. A subset A of (X, µ) is called supra generalized locally closed set (briefly supra g-locally closed set), if A=U V, where U is supra g-open in (X, µ) and V is supra g-close ...
... generalized locally closed sets and discuss some of their properties. 3.1 Definition Let (X, µ) be a supra topological space. A subset A of (X, µ) is called supra generalized locally closed set (briefly supra g-locally closed set), if A=U V, where U is supra g-open in (X, µ) and V is supra g-close ...
MONODROMY AND FAITHFUL REPRESENTABILITY OF LIE
... and second-countable. (If one prefers to allow manifolds and Lie groups to have uncountably many components - as some authors do - one could relax the assumption of second-countability of smooth manifolds by the condition of paracompactness.) A C ∞ -groupoid is a topological groupoid G , together wi ...
... and second-countable. (If one prefers to allow manifolds and Lie groups to have uncountably many components - as some authors do - one could relax the assumption of second-countability of smooth manifolds by the condition of paracompactness.) A C ∞ -groupoid is a topological groupoid G , together wi ...
