Product topology - Wikipedia
In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
By default, on ÛXl always take the product topology. Recall : Let X and Y be topological spaces; let f : X ® Y be a bijection. If both the function f and the inverse function : Y ® X are continuous, then f is called a homeomorphism.
Product Topology -- from Wolfram MathWorld
6 天之前 · This definition extends in a natural way to the Cartesian product of any finite number n of topological spaces. The product topology of R×...×R_ ()_ (n times), where R is the real line with the Euclidean topology, coincides with the Euclidean topology of the Euclidean space R^n.
elementary set theory - Definition of Product Topology ...
Definition of Product Topology. Definition: If X X and Y Y are topological spaces. The product topology on X × Y X × Y is the topology having basis the collection B B of all sets of the form U × V U × V, where U U is an open set of X X and V V is an open set of Y Y.
2016年5月30日 · The product topology on set X×Y is the topology having as basis the collection B of all sets of the form U ×V, where U is an open subset of X and V is an open subset of Y.
Product topology The aim of this handout is to address two points: metrizability of nite products of metric spaces, and the abstract characterization of the product topology in terms of universal mapping properties among topological spaces.
The product topology is sometimes called the “Tychonoff topology.” We always assume that a product of topological spaces has the product topol#\α ogy unless some other topology is explicitly stated. Because the product topology is a weak topology, a subbase consists of all sets of form 'Y ( œ ÒY Ó Y \ Þα α α α1α