Cardinality Estimations of Sets with Interval Uncertainties in Finite Topological Spaces

Topology, Metric Spaces and the Generalized Continuum Hypothesis

This is a paper that aims to interpret the cardinality of a set in terms of Baire Category, i.e. how many closed nowhere dense sets can be deleted from a set before the set itself becomes negligible. . To do this natural tree-theoretic structures such as the Baire topology are introduced, and the Baire Category Theorem is extended to a statement that a $\aleph$-sequentially complete binary tree representation of a Hausdorff topological space that has a clopen base of cardinality $\aleph$ and no isolated or discrete points is not the union of $<\aleph+1$-many nowhere dense subsets for cardinal …