International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 407-409
doi:10.1155/S0161171281000264
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
Abstract
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.