Topological Algebra

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2 domain-specific abstractions whose origin domain is Topological Algebra.

• Direct Sum of Topological Groups — Decompose a topological group into subgroup factors whose multiplication map is simultaneously a group isomorphism and a homeomorphism, preserving both algebraic and topological structure.
• Hausdorff completion — The inverse-limit completion of a filtered group formed from its discrete quotients, with the filtration intersection removed by the canonical map.