![arXiv:1205.2342v1 [math.GR] 10 May 2012 Homogeneous compact](http://s1.studyres.com/store/data/014455921_1-3cd5e27d3d632291f2fbeb8ac68a29b6-300x300.png)
important result of the fuzzy tychonoff theorem and
... Much of topology can be done in a setting where open sets have “fuzzy boundaries.” To render this precise; the ...
... Much of topology can be done in a setting where open sets have “fuzzy boundaries.” To render this precise; the ...
splitting closure operators - UWC Mathematics Department
... countable function approximation property ([4], Theorem 2.8). A Tychonoff space is said to satisfy the countable function approximation property if for each real valued function f : X → R there exists a sequence (fn : X → R) of continuous maps such that for each finite subset F of X and ε > 0 ther ...
... countable function approximation property ([4], Theorem 2.8). A Tychonoff space is said to satisfy the countable function approximation property if for each real valued function f : X → R there exists a sequence (fn : X → R) of continuous maps such that for each finite subset F of X and ε > 0 ther ...
1 Well-ordered sets 2 Ordinals
... Jech [Jec03], but you can probably find it in any reasonable set theory book. The rest is from Hovey’s book Model Categories [Hov99]. ...
... Jech [Jec03], but you can probably find it in any reasonable set theory book. The rest is from Hovey’s book Model Categories [Hov99]. ...
COMPACT METRIZABLE STRUCTURES AND CLASSIFICATION
... Proposition (See Proposition 1). For any countable relational language L, the relation of homeomorphic isomorphism between compact metrizable L-structures is Borel bireducible with the complete orbit equivalence relation Egrp induced by a Polish group action. The novelty here is that the relation of ...
... Proposition (See Proposition 1). For any countable relational language L, the relation of homeomorphic isomorphism between compact metrizable L-structures is Borel bireducible with the complete orbit equivalence relation Egrp induced by a Polish group action. The novelty here is that the relation of ...
On different notions of tameness in arithmetic geometry
... One says that an étale covering C 0 → C is tamely ramified along C̄ r C if for every x ∈ C̄ r C the valuation v x is tamely ramified in k(C 0 )|k(C ). Since the proper, regular curve C̄ is determined by C, we can say that the étale covering C 0 → C is tame if it is tamely ramified along C̄ r C. Foll ...
... One says that an étale covering C 0 → C is tamely ramified along C̄ r C if for every x ∈ C̄ r C the valuation v x is tamely ramified in k(C 0 )|k(C ). Since the proper, regular curve C̄ is determined by C, we can say that the étale covering C 0 → C is tame if it is tamely ramified along C̄ r C. Foll ...
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.