International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 407-409

A characterization of pseudocompactness

Prabduh Ram Misra1 and Vinodkumar2

1I.M.F., U.F.G., Caixa Postal – 597, Goiânia 74000, Go, Brazil
2I.I.T., New Delhi, India

Received 6 October 1980

Copyright © 1981 Prabduh Ram Misra and Vinodkumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.