Proof That a Cartesian Product of Bases is a Basis For The Product


Ifis a basis for a a topological spaceandis a basis for a a topological spacethen is a basis for a the topological space


Supposeis open. Thenis the union of cartesian productswhereandare open inrespectively hence

is a basis ofandis a basis forso for eachandwhere


The setis the required basis for