In the work using interval mathematics, we develop knowledge for cardinal numbers from the viewpoint of uncertainty analysis. In the finite non-T 1 topological spaces, the inclusion-exclusion formula provide interval estimations for the closure and interior of given sets. This paper introduces a novel approach that combines combinatorial and point-set topology, which leads to a number of results. Among these is the cardinality estimation for the intersection of two open sets that cover a hyperconnected topo-logical space.