Compactness and separation for represented spaces

Details Compactness and separation for represented spaces Compactness and separation for represented spaces

2012-04-17

arxiv.org/abs/1204.3763v1

Mathematics

Logic

Scientific paper

The effective notions of compactness and topological separation are studied in full generality for represented spaces. Each concept is characterized by a multitude of equivalent properties, each corresponding the computability or continuity of certain functions. In particular, admissibility is identified as the effective counterpart to T_0 separation. A synthetic approach allows simple proofs of strong results compared to the previous literature.

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