Topological vector e is vector e over topological field (most often the real or complex numbers with their standard topologies) that is endowed with topology such that vector addition and scalar multiplication are continuous functions (where the domains of these functions are endowed with product .In topology and related branches of mathematics, topological e may be defined as set of points, along with set of neighbourhoods for each point, satisfying set of axioms relating points and neighbourhoods. Topology examples example let be the cl of subsets of consisting of set of rationals and irrationals and all open infinite interval of the form $_{}$= (, $infty$) where $epsilon$ . show that is topology on . . topological vector es .denitions banach es, and more generally normed es, are endowed with two structures linear .

Those examples often possess other structures in addition to topology and this pro vides the key link between topology and other branches of geometry . the will serv as ilrations and the testing ground for the notions and The discrete topology is the strongest topology on set, while the trivial topology is the weakest. finite examples finite sets can have many topologies on them. Topology examples example let be the cl of subsets of consisting of set of rationals and irrationals and all open infinite interval of the form $_{}$= (, $infty$) where $epsilon$ . show that is topology on . . topological vector es .denitions banach es, and more generally normed es, are endowed with two structures linear . Those examples often possess other structures in addition to topology and this pro vides the key link between topology and other branches of geometry . the will serv as ilrations and the testing ground for the notions and

The discrete topology is the strongest topology on set, while the trivial topology is the weakest. finite examples finite sets can have many topologies on them.