Noetherian Quasi-Polish Spaces
Matthew de Brecht, Arno Pauly

TL;DR
This paper characterizes Noetherian Quasi-Polish spaces using a new concept called bla-compactness, linking higher-order compactness notions with classical topological properties within a computable framework.
Contribution
It introduces bla-compactness as a higher-order analogue of compactness and fully characterizes Noetherian Quasi-Polish spaces through this concept.
Findings
bla-compactness preserves bla-2 predicates.
Noetherian Quasi-Polish spaces are exactly bla-compact.
The characterization applies to a broad class of examples.
Abstract
In the presence of suitable power spaces, compactness of can be characterized as the singleton being open in the space of open subsets of . Equivalently, this means that universal quantification over a compact space preserves open predicates. Using the language of represented spaces, one can make sense of notions such as a -subset of the space of -subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces where is a -subset of the space of -subsets of . Call this notion -compactness. As is self-dual, we find that both universal and existential quantifier over -compact spaces preserve predicates. Recall that a space is called Noetherian iff every…
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