Problems in the Theory of Convergence Spaces

摘要: We investigate several problems in the theory of convergence spaces: generalization Kolmogorov separation from topological spaces to spaces, representation reflexive digraphs as construction differential calculi on mereology and a universal homogeneous pretopological space. First, we generalize spaces; then study properties spaces. Second, develop which specialize Cayley graphs. Third, conservatively extend concept classical analysis arbitrary use this extension obtain for finite groups, Boolean hypercubes, labeled graphs, Cantor tree, real binary sequences. Fourth, show that standard axiomatization is equivalent condition space discrete, consequently, any model general extensional indistinguishable set theory; these results cartesian closed category Finally, every can be embedded into space; result construct Problems Theory Convergence Spaces by Daniel R. Patten B.A., Utica College Syracuse University, 2001 M.S., 2004 2013