On $$\kappa $$-Pseudocompactess and Uniform Homeomorphisms of Function Spaces

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