Given a set of this type in a function's target space, the functionis continuous if and only if the preimage of every element of this set is open.
In functional analysis, two types of this concept differ in whether they allow for infinite sums or not;those are the Schauder and Hamel types. Given a set of this type in a function's target space, the functionis continuous if and only if the preimage of every element of this set is open. A free module is a moduleequipped with a set of this type. Taking unions of elements from this set yields all (*) elements of a topology.An algorithm for modifying a set of this type forms an element "u sub n" by taking "v sub n" and subtracting theprojections of each previous "u sub i" onto "v sub n;" that orthonormalization is called the Gram-Schmidt process.The "standard" one for Rn ("R-n") is the set of unit vectors, and the number of elements in this set equals thedimension of a vector space. For 10 points, give this term for a set of linearly independent vectors that span a vectorspace.
In functional analysis, two types of this concept differ in whether they allow for infinite sums or not;those are the Schauder and Hamel types.
basis