New proofs of theorems of Michael and Worrell

• James E. Joseph Howard University
• Bhamini M. P. Nayar Morgan Sate University
Keywords: paracpmpact spaces; metacompact spaces, collectionwise normal spaces

Abstract

New proofs of theorems of Michael and Worrell, that paracompactness and metacompactness are closed continuous invariants are presented here. A result due to Joseph and Kwack that all open sets in $$Y$$ have the form $$g(V)-g(X-V)$$, where $$V$$ is open in $$X$$, if $$g:X\to Y$$ is continuous, closed and onto is used to give the new proofs.