WebIn mathematics, a double cover or double covering may refer to: Double cover (topology), a two-to-one mapping from one topological space to another. Frequently occurring special cases include The orientable double cover of a non-orientable manifold The bipartite double cover of an undirected graph G, formed by the graph tensor … Covers are commonly used in the context of topology. If the set $${\displaystyle X}$$ is a topological space, then a cover $${\displaystyle C}$$ of $${\displaystyle X}$$ is a collection of subsets $${\displaystyle \{U_{\alpha }\}_{\alpha \in A}}$$ of $${\displaystyle X}$$ whose union is the whole space … See more In mathematics, and more particularly in set theory, a cover (or covering) of a set $${\displaystyle X}$$ is a family of subsets of $${\displaystyle X}$$ whose union is all of $${\displaystyle X}$$. More formally, if A subcover of a … See more The language of covers is often used to define several topological properties related to compactness. A topological space X is said to be Compact if every … See more • Atlas (topology) – Set of charts that describes a manifold • Bornology – Mathematical generalization of boundedness See more A refinement of a cover $${\displaystyle C}$$ of a topological space $${\displaystyle X}$$ is a new cover $${\displaystyle D}$$ of $${\displaystyle X}$$ such … See more A topological space X is said to be of covering dimension n if every open cover of X has a point-finite open refinement such that no point of X is included in more than n+1 sets in the … See more • "Covering (of a set)", Encyclopedia of Mathematics, EMS Press, 2001 [1994] See more
What are some simple examples illustrating the definition of "cover"
WebMar 21, 2013 · If you want to say closer to topology, you introduce étale coverings, which are non-ramified and flat coverings. Coming back to the general definition, note that a covering p: Y → X between irreducible varieties induces a finite field extension p ∗: k ( X) → k ( Y) of their function fields. This finally allows to answer your question : WebDec 17, 2014 · Given an open cover of the covering space, refine the cover to obtain a new open cover where every open set in the new cover maps homeomorphically onto an open set in the base space, and the pullback of the neighborhood is a disjoint union of k homeomorphic neighborhoods, where the cover has k sheets, and each of the disjoint … prince william shouted at prince charles
Covering problems - Wikipedia
WebFeb 14, 2024 · A family of nonempty subsets of whose union contains the given set (and which contains no duplicated subsets) is called a cover (or covering) of . For example, there is only a single cover of , namely . However, there are five covers of , namely , , , , and . WebSep 4, 2024 · So assume p: X ~ → X be a covering map where X ~ is path-connected. Then in exercise 53.3 inMunkres' topology book, if we have a finite fiber, say k many, at some … WebOne can easily cover the vertices of the n-cube by 2 hyperplanes. Here it is proved that any set of hyperplanes that covers all the vertices of the n-cube but one contains at least n hyperplanes. We give a variety of proofs and generalizations. All Science Journal Classification (ASJC) codes Discrete Mathematics and Combinatorics Fingerprint prince william shooting