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_\ka...

In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensions. Rogers’ definitions focussed on a specific representation of higher dimensional trees. This paper pres...