Search results
Results From The WOW.Com Content Network
The disjoint union space X, together with the canonical injections, can be characterized by the following universal property: If Y is a topological space, and f i : X i → Y is a continuous map for each i ∈ I, then there exists precisely one continuous map f : X → Y such that the following set of diagrams commute:
In mathematics, the disjoint union (or discriminated union) of the sets A and B is the set formed from the elements of A and B labelled (indexed) with the name of the set from which they come. So, an element belonging to both A and B appears twice in the disjoint union, with two different labels.
In graph theory, a cograph, or complement-reducible graph, or P 4-free graph, is a graph that can be generated from the single-vertex graph K 1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K 1 and is closed under complementation and disjoint union.
λ-system (Dynkin system) – Family closed under complements and countable disjoint unions; π-system – Family of sets closed under intersection; Ring of sets – Family closed under unions and relative complements; Russell's paradox – Paradox in set theory (or Set of sets that do not contain themselves)
A wedge sum of two circles. In topology, the wedge sum is a "one-point union" of a family of topological spaces.Specifically, if X and Y are pointed spaces (i.e. topological spaces with distinguished basepoints and ) the wedge sum of X and Y is the quotient space of the disjoint union of X and Y by the identification : = /,
The important special case where the family of maps consists of a single surjective map can be completely characterized using the notion of quotient map.A surjective function : (,) (,) between topological spaces is a quotient map if and only if the topology on coincides with the final topology induced by the family = {}.
Let be the least uncountable ordinal.In an analog of Baire space derived from the -fold cartesian product of with itself, any closed set is the disjoint union of an -perfect set and a set of cardinality, where -closedness of a set is defined via a topological game in which members of are played.
In general, an n-dimensional CW complex is constructed by taking the disjoint union of a k-dimensional CW complex (for some <) with one or more copies of the n-dimensional ball. For each copy, there is a map that "glues" its boundary (the ( n − 1 ) {\displaystyle (n-1)} -dimensional sphere ) to elements of the k {\displaystyle k} -dimensional ...