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

对于拓扑空间X，其在类中的反射$\mathsf{Ť}$ 拓扑空间是一对 $（\mathsf{Ť}X，{\mathrm{一世}}_X）$ 由一个空间组成 $\mathsf{Ť}X\in \mathsf{Ť}$ 和一个连续的地图 ${\mathrm{一世}}_X：X\to \mathsf{Ť}X$ 这样对于任何连续图 $F：X\to ÿ$ 到一个空间 $ÿ\in \mathsf{Ť}$ 存在一个独特的连续图 $\overline{F}：\mathsf{Ť}X\to ÿ$ 这样 $F=\overline{F}\circ {\mathrm{一世}}_X$。本文提出了一个无限基数κ和非空集中号的超滤器κ，我们研究拓扑空间中的类的反射${\mathsf{H}}_{\kappa }$的κ -bounded Hausdorff空间${\mathsf{H}}_{\mathrm{中号}}$的中号-Compact Hausdorff空间（一个拓扑空间X就是κ -bounded如果基数≤子集的封闭件κ中X是紧凑的; X是M-紧凑如果任何功能$X：\kappa \to X$每个超滤器在X中都有一个p极限$p\in \mathrm{中号}$）。