  By de Vries duality, the category of compact Hausdorff spaces is dually
equivalent to the category of de Vries algebras. In our recent article, we have
extended de Vries duality to completely regular spaces by generalizing de Vries
algebras to de Vries extensions. To illustrate the utility of this point of
view, we show how to use this new duality to obtain algebraic counterparts of
normal and locally compact Hausdorff spaces in the form of de Vries extensions
that are subject to additional axioms which encode the desired topological
property. This, in particular, yields a different perspective on de Vries
duality. As a further application, we show that a duality for locally compact
Hausdorff spaces due to Dimov can be obtained from our approach.
