A是拓扑空间X中闭集,B是拓扑空间Y中闭集,证明:A×B是X×Y中闭集

问题描述:

A是拓扑空间X中闭集,B是拓扑空间Y中闭集,证明:A×B是X×Y中闭集

X-A is open in X, and Y-B is open in Y.
Hence (X-A) ×B and X ×(Y-B) are open in X×Y
So A×B = X×Y - (X-A) ×B - X ×(Y-B) is closed in X×Y.