generalizations of borsuk-ulam theorem
... Conner-Floyd proved in their book [1] the following theorem which is a generalization of the classical Borsuk-Ulam theorem: Let /: Sn^>M be a continuous map of the n-sphere to a differentiable manifold of dimension m, and T be a fixed point free differentiable involution on Sn. Assume that m^n and / ...
... Conner-Floyd proved in their book [1] the following theorem which is a generalization of the classical Borsuk-Ulam theorem: Let /: Sn^>M be a continuous map of the n-sphere to a differentiable manifold of dimension m, and T be a fixed point free differentiable involution on Sn. Assume that m^n and / ...
Redalyc.On a- t-disconnectedness and α- τ
... There are several natural approaches that can take to rigorously the concepts of connectedness for a topological spaces. Two most common approaches are connected and path connected and these concepts are applicable Intermediate Mean Value Theorem and use to help distinguish topological spaces. These ...
... There are several natural approaches that can take to rigorously the concepts of connectedness for a topological spaces. Two most common approaches are connected and path connected and these concepts are applicable Intermediate Mean Value Theorem and use to help distinguish topological spaces. These ...
GEOMETRY 5: Set-theoretic topology.
... Definition 5.13. Let M be a topological space and Z ⊂ M be an infinite subset. A point x ∈ M is called an accumulation point of Z, if every neighborhood of x contains some point z ∈ Z. A limit of a sequence {xi } is defined to be a point x such that every neighborhood of x contains almost all xi ’s. ...
... Definition 5.13. Let M be a topological space and Z ⊂ M be an infinite subset. A point x ∈ M is called an accumulation point of Z, if every neighborhood of x contains some point z ∈ Z. A limit of a sequence {xi } is defined to be a point x such that every neighborhood of x contains almost all xi ’s. ...
Fibre products
... Before proving this, let us understand some consequences. First of all, it tells us that products exist. Since Spec Z is the terminal object in the category of schemes. The product is X ⇥ Y = X ⇥Spec Z Y . Secondly, given a point s 2 S of a scheme, and a morphism f : X ! S, we want to put a natural ...
... Before proving this, let us understand some consequences. First of all, it tells us that products exist. Since Spec Z is the terminal object in the category of schemes. The product is X ⇥ Y = X ⇥Spec Z Y . Secondly, given a point s 2 S of a scheme, and a morphism f : X ! S, we want to put a natural ...
K(n)-COMPACT SPHERES H˚ akon Schad Bergsaker Contents
... of the various skeleta of BG from the bar spectral sequence. We also need some standard formulas for the p-order of an integer. In section 6 we will try to construct new examples of K(n)-compact groups. To do this we need to calculate the K(n)-cohomology of a loop space, and we do this with a K(n)-b ...
... of the various skeleta of BG from the bar spectral sequence. We also need some standard formulas for the p-order of an integer. In section 6 we will try to construct new examples of K(n)-compact groups. To do this we need to calculate the K(n)-cohomology of a loop space, and we do this with a K(n)-b ...
on generalizations of regular-lindelöf spaces
... semiregular, by [3, Proposition 3.4], X is weakly Lindelöf. Corollary 4.3. Let (X, τ) be a regular space. Then (X, τ) is weakly Lindelöf if and only if (X, τ) is weakly regular-Lindelöf. Proposition 4.4. If (X, τ) is regular and nearly paracompact, then (X, τ) is Lindelöf if and only if (X, τ) is we ...
... semiregular, by [3, Proposition 3.4], X is weakly Lindelöf. Corollary 4.3. Let (X, τ) be a regular space. Then (X, τ) is weakly Lindelöf if and only if (X, τ) is weakly regular-Lindelöf. Proposition 4.4. If (X, τ) is regular and nearly paracompact, then (X, τ) is Lindelöf if and only if (X, τ) is we ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.