Pohlke's theorem

Pohlke's theorem is a result in the field of topology, specifically in the study of connected spaces. It states that if \(X\) is a connected space and \(Y\) is a connected subspace of \(X\), then \(X\) is connected if and only if the union of \(Y\) with any other connected subspace \(Z\) of \(X\) is connected.