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The new computational paradigm of conceptual computation has been introducedin the research program of Artificial Mathematical Intelligence. We provide theexplicit artificial generation (or conceptual computation) for the fundamentalmathematical notion of topological groups. Specifically, we start with twobasic notions belonging to topology and abstract algebra, and we describerecursively formal specifications in the Common Algebraic SpecificationLanguage (CASL). The notion of conceptual blending between such conceptualspaces can be materialized computationally in the Heterogeneous Tool Set(HETS). The fundamental notion of topological groups is explicitly generatedthrough three different artificial specifications based on conceptual blendingand conceptual identification, starting with the concepts of continuousfunctions and mathematical groups (described with minimal set-theoreticalconditions). This constitutes in additional heuristic evidence for the thirdpillar of Artificial Mathematical Intelligence.

Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence