High Quality Content by WIKIPEDIA articles! Computable topology studies the topological and algebraic structure of computation. Computable topology includes algorithmic topology and therefore encompasses computer science. Computational topology is equivalent to the topology of ?-calculus. Within computer science computational forms can be reduced to ?-calculus's functional based mathematics. As shown by Allan Turing and Alonzo Church, the ?-calculus is strong enough to describe all mechanically computable functions (see Church-Turing thesis). Lambda-calculus is then a foundational mathematics easily made into a principle programming language from which other languages can be built. For this reason when considering the topology of computation it is suitable to focus on the topology of ?-calculus. Functional programming, e.g. type free lambda Calculus, originated as a theoretical foundation of mathematics. The premise relies on functional computability, where objects and functions are...

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