Geodesic
Completeness: When Enough is Enough
Documenta mathematica, Tome 24 (2019), pp. 899-914
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We investigate the notion of a complete enough metric space that, while classically vacuous, in a constructive setting allows for the generalisation of many theorems to a much wider class of spaces. In doing so, this notion also brings the known body of constructive results significantly closer to that of classical mathematics. Most prominently, we generalise the Kreisel-Lacome-Shoenfield Theorem/Tseytin's Theorem on the continuity of functions in recursive mathematics.
DOI : 10.4171/dm/696
Classification : 03D78, 03F55, 03F60
Mots-clés : completeness, constructive mathematics, computable analysis 
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     author = {Hannes Diener and Matthew Hendtlass},
     title = {Completeness: {When} {Enough} is {Enough}},
     journal = {Documenta mathematica},
     pages = {899--914},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/696},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/696/}
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Hannes Diener; Matthew Hendtlass. Completeness: When Enough is Enough. Documenta mathematica, Tome 24 (2019), pp. 899-914. doi: 10.4171/dm/696

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