  A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every
continuous mapping $f$ of $X$ into $\mathbb{R}^\kappa$ the image $f(X)$ is
compact. This notion generalizes pseudocompactness and gives a stratification
of spaces lying between pseudocompact and compact spaces. It is well known that
pseudocompactness of $X$ is determined by the uniform structure of the function
space $C_p(X)$ of continuous real-valued functions on $X$ endowed with the
pointwise topology. In respect of that A.V. Arhangel'skii asked in [Topology
Appl., 89 (1998)] if analogous assertion is true for
$\kappa$-pseudocompactness. We provide an affirmative answer to this question.

General Topology