Generalized Finite Sequence of Fuzzy Topographic Topological Mapping

Problem statement: Fuzzy Topographic Topological Mapping (FTTM) was developed to solve the neuromagnetic inverse problem. FTTM consisted of four topological spaces and connected by three homeomorphisms. FTTM 1 and FTTM 2 were developed to present 3-D view of an unbounded single current source and bounded multicurrent sources, respectively. FTTM 1 and FTTM 2 were homeomorphic and this homeomorphism will generate another 14 FTTM. We conjectured if there exist n elements of FTTM, then the numbers of new elements are n⁴-n. Approach: In this study, the conjecture was proven by viewing FTTMs as sequence and using its geometrical features. Results: In the process, several definitions were developed, geometrical and algebraic properties of FTTM were discovered. Conclusion: The conjecture was proven and some features of the sequence appear in Pascal Triangle.