Different proofs of theorems of Michael and Worrell

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Terrence A. Edwards
James E. Joseph
Bhamini M. P. Nayar


Different proofs of theorems of E. Michael and J. M. 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 these proofs. Also a characterization that a space is paracompact (metacompact) if and only if every ultrafilter of type \(P\) (type \(M\)) converges [5], is used to give another proof of the invariance of paracompactness and metacompactness under continuous closed surgections.

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Edwards, T. A. ., Joseph, J. E. ., & Nayar, B. M. P. . (2022). Different proofs of theorems of Michael and Worrell. Journal of Advanced Studies in Topology, 10(1), 58–61. Retrieved from https://m-sciences.com/index.php/jast/article/view/261
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