Editing Projection (linear algebra) (section)

===Open map===
Every projection is an [[open map]] onto its image, meaning that it maps each [[open set]] in the [[Domain of a function|domain]] to an open set in the [[subspace topology]] of the [[image (mathematics)|image]].{{cn|date=November 2022}}  That is, for any vector <math>\mathbf{x}</math> and any ball <math>B_\mathbf{x}</math> (with positive radius) centered on <math>\mathbf{x}</math>, there exists a ball <math>B_{P\mathbf{x}}</math> (with positive radius) centered on <math>P\mathbf{x}</math> that is wholly contained in the image <math>P(B_\mathbf{x})</math>.