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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.
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