FUNDAMENTAL GROUPS OF TOPOLOGICAL STACKS
... see Theorem 9.1, Theorem 10.4, and Remark 10.7 – Corollary 10.5 should also be of interest. For the above results to hold, one needs a technical hypothesis which is called the slice condition (Definitions 5.1 and 5.4). As the terminology suggests, this notion is modeled on the slice property of comp ...
... see Theorem 9.1, Theorem 10.4, and Remark 10.7 – Corollary 10.5 should also be of interest. For the above results to hold, one needs a technical hypothesis which is called the slice condition (Definitions 5.1 and 5.4). As the terminology suggests, this notion is modeled on the slice property of comp ...
General Topology - Institut for Matematiske Fag
... Sets and maps This chapter is concerned with set theory which is the basis of all mathematics. Maybe it even can be said that mathematics is the science of sets. We really don’t know what a set is but neither do the biologists know what life is and that doesn’t stop them from investigating it. 1. Se ...
... Sets and maps This chapter is concerned with set theory which is the basis of all mathematics. Maybe it even can be said that mathematics is the science of sets. We really don’t know what a set is but neither do the biologists know what life is and that doesn’t stop them from investigating it. 1. Se ...
Real Analysis: Part II - University of Arizona Math
... The theory of pseudometric spaces is much the same as the theory of metric spaces. The main difference is that a sequence can converge to more than one limit. However each two limits of the sequence have distance zero from each other, so this does not matter too much. Given a pseudometric space P , ...
... The theory of pseudometric spaces is much the same as the theory of metric spaces. The main difference is that a sequence can converge to more than one limit. However each two limits of the sequence have distance zero from each other, so this does not matter too much. Given a pseudometric space P , ...
Normality on Topological Groups - Matemáticas UCM
... discrete in X. In order to see that Y is discrete, it is enough to define a continuous character in G which takes the value −1 in yα and 1 in yβ for every β ∈ A \ {α}. Consider first ϕ : Z → T, the character on Z such that ϕ(n) = eπni , ∀n ∈ Z. It gives rise to characters on ZR , just composing with ...
... discrete in X. In order to see that Y is discrete, it is enough to define a continuous character in G which takes the value −1 in yα and 1 in yβ for every β ∈ A \ {α}. Consider first ϕ : Z → T, the character on Z such that ϕ(n) = eπni , ∀n ∈ Z. It gives rise to characters on ZR , just composing with ...
Repovš D.: Topology and Chaos
... Poincaré developed topology and exploited this new branch of mathematics in ingenious ways to study the properties of differential equations. Ideas and tools from this branch of mathematics are particularly well suited to describe and to classify a restricted but enormously rich class of chaotic dyn ...
... Poincaré developed topology and exploited this new branch of mathematics in ingenious ways to study the properties of differential equations. Ideas and tools from this branch of mathematics are particularly well suited to describe and to classify a restricted but enormously rich class of chaotic dyn ...
General Topology
... Definition A1.8 Let X be a metric space, let (xn )∞ n=1 be a sequence in X, and let x ∈ X. Then (xn ) converges to x if d(xn , x) → 0 as n → ∞. Explicitly, then, (xn ) converges to x if and only if: for all ε > 0, there exists N ≥ 1 such that for all n ≥ N , d(xn , x) < ε. This generalizes the defin ...
... Definition A1.8 Let X be a metric space, let (xn )∞ n=1 be a sequence in X, and let x ∈ X. Then (xn ) converges to x if d(xn , x) → 0 as n → ∞. Explicitly, then, (xn ) converges to x if and only if: for all ε > 0, there exists N ≥ 1 such that for all n ≥ N , d(xn , x) < ε. This generalizes the defin ...
A survey of ultraproduct constructions in general topology
... theorem) and T. Skolem (who was building nonstandard models of arithmetic), it was not until 1955, when J. Loś published his fundamental theorem of ultraproducts, that the construction was described explicitly, and its importance to first-order logic became apparent. The understanding of the struct ...
... theorem) and T. Skolem (who was building nonstandard models of arithmetic), it was not until 1955, when J. Loś published his fundamental theorem of ultraproducts, that the construction was described explicitly, and its importance to first-order logic became apparent. The understanding of the struct ...
