Spaces {function space} can have functions as points or distances. Spaces can have finite numbers of elements. Spaces can have infinite numbers of elements, with two limiting elements at interval ends {closed set, function}. Spaces can have no sequence gaps {sequentially compact}. Spaces can have only one limit element {relatively sequentially compact}.
Function spaces can use generalized Pythagorean theorem.
Function spaces can have triangle inequality, Schwarz's inequality, and other inequalities {Bessel's inequality}.
Mutually orthogonal space elements are linearly independent.
Mathematical Sciences>Calculus>Analysis>Space
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Date Modified: 2022.0224