  According to a folklore characterization of supercompact spaces, a compact
Hausdorff space is supercompact if and only if it has a binary closed
$k$-network. This characterization suggests to call a topological space $super$
if it has a binary closed $k$-network $\mathcal N$. The binarity of $\mathcal
N$ means that every linked subfamily of $\mathcal N$ is centered. Therefore, a
Hausdorff space is supercompact if and only if it is super and compact. In this
paper we prove that the class of super spaces contains all GO-spaces, all
supercompact spaces, all metrizable spaces, and all collectionwise normal
$\aleph$-spaces. Moreover, the class of super spaces is closed under taking
Tychonoff products and discretely dense sets in Tychonoff products. The
superness of metrizable spaces implies that each compact metrizable space is
supercompact, which was first proved by Strok and Szyma\'nski (1975) and then
reproved by Mills (1979), van Douwen (1981), and D{\c e}bski (1984).

General Topology