Let us call a function f from a space X into a space Y preserving if the image of every compact subspace of X is compact in Y and the image of every connected subspace of X is connected in Y. By elementary theorems a continuous function is always preserving. Evelyn R. McMillan proved in 1970 that if X is Hausdorff, locally connected and Frèchet, Y is Hausdorff, then the converse is also true: any preserving function f:X --> Y is continuous. The main result of this paper is that if X is any product of connected linearly ordered spaces (e.g. if X=R\kappa) and f:X --> Y is a preserving function into a regular space Y, then f is continuous.
Mathematics Subject Classification. 54C05 54D05 54F05 54B10.
Keywords. Hausdorff space, continuity, compact, connected, locally connected, Frechetspace, monotonically normal, linearly ordered space.
Comments. This article has been submitted for publication to Fundamenta Mathematicae.