# New proofs of theorems of Michael and Worrell

• James E. Joseph Howard University
• Bhamini M. P. Nayar Morgan Sate University

### 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.

Published
2017-02-18
How to Cite
JOSEPH, James E.; NAYAR, Bhamini M. P.. New proofs of theorems of Michael and Worrell. Journal of Advanced Studies in Topology, [S.l.], v. 8, n. 1, p. 21-23, feb. 2017. ISSN 2090-388X. Available at: <http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1220>. Date accessed: 20 aug. 2017. doi: https://doi.org/10.20454/jast.2017.1220.
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