Computable Topology
Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be confused with algorithmic or ''computational topology'', which studies the application of computation to topology. Topology of lambda calculus As shown by Alan Turing and Alonzo Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis). Lambda-calculus is thus effectively a programming language, from which other languages can be built. For this reason when considering the topology of computation it is common to focus on the topology of λ-calculus. Note that this is not necessarily a complete description of the topology of computation, since functions which are equivalent in the Church-Turing sense may still have different topologies. The topology of λ-calculus is the Scott topology, and when restricted to continuous functions the type free λ-calculus amounts to a to ...
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