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.

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Published
2017-02-18
How to Cite
Joseph, J. E., & Nayar, B. M. P. (2017). New proofs of theorems of Michael and Worrell. Journal of Advanced Studies in Topology, 8(1), 21-23. https://doi.org/10.20454/jast.2017.1220
Section
Original Articles