*Definition [#g1ef36ed]
-A topological space X is m-pseudocompact if each map (continuous function) f:X→R^m has a compact range, where R^m denotes the Cartesian product of the reals m times (m is a cardinal).


*Property [#ndab8452]
-completely regular, Hausdorff space is [[m-quasicompact]] if and only if it is m-pseudocompact.
-Let X be a linearly ordered space, and let m be an infinite carinal. The following are then equivalent:
++ X is m-bounded
++ X is m-compact
++ X is m-pseudocompact
++ X is [[m-quasicompact]]
++ For each gap u of X, |ω_{α(u)}|>m and |ω_{β(u)}|>m .

*Reference [#g998b14c]
Gulden, S. L. , Fleischman, W. M. and Weston, J. H. ,''Linearly ordered topological spaces'', 
Proc. Amer. Math. Soc. 24 1970 197--203.