(related to Proposition: Alternative Characterization of Topological Spaces)

- By applying the De Morgan rules to the set $\mathcal C$ we get exactly the definition of a topology based on open subsets of $X.$
- Thus $(X,\mathcal C)$ is a topological space.∎

**Steen, L.A.;Seebach J.A.Jr.**: "Counterexamples in Topology", Dover Publications, Inc, 1970**Jänich, Klaus**: "Topologie", Springer, 2001, 7th Edition