On ?-bounded and M-compact reflections of topological spaces

For a topological space $X$ its reflection in class $\mathsf T$ of spaces is pair $(\mathsf T X,i_X)$ consisting X\in\mathsf and continuous map $i_X:X\to \mathsf X$ such that for any $f:X\to Y$ to $Y\in\mathsf there exists unique $\bar f:\mathsf X\to $f=\bar f\circ i_X$. In this paper an infinite cardinal $\kappa$ nonempty set $M$ ultrafilters on $\kappa$, we study the reflections classes H_\kappa$ $\kappa$-bounded Hausdorff H_M$ $M$-compact (a if closures subsets cardinality $\le\kappa$ are compact; function $x:\kappa\to has $p$-limit every ultrafilter $p\in M$).