Comparing computability in two topologies

Autor: DJAMEL EDDINE AMIR, MATHIEU HOYRUP

Computable analysis provides ways of representing points in a topological space, and therefore of defining a notion of computable points of the space. In this article, we investigate when two topologies on the same space induce different sets of comp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9f52d3c233f4913ab200cf6deca1cb8
https://inria.hal.science/hal-03702999/file/article.pdf

Statures and Sobrification Ranks of Noetherian Spaces

Autor: Goubault-Larrecq, Jean, Laboureix, Bastien

Publikováno v: Houston Journal of Mathematics
Houston Journal of Mathematics, In press, 49 (1), pp.1-76

There is a rich theory of maximal order types of well-partial-orders (wpos), pioneered by de Jongh and Parikh (1977) and Schmidt (1981). Every wpo is Noetherian in its Alexandroff topology, and there are more; this prompts us to investigate an analog

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8642554e38282bc5e040252b63a16fe2
https://inria.hal.science/hal-04138338/file/01goubaultlarrecq.pdf

Continuous R-valuations

Autor: Goubault-Larrecq, Jean, Jia, Xiaodong

Publikováno v: Electronic Notes in Theoretical Informatics and Computer Science
Electronic Notes in Theoretical Informatics and Computer Science, In press, 2, ⟨10.46298/entics.proceedings.isdt9⟩
9th International Symposium on Domain Theory
9th International Symposium on Domain Theory, Jul 2022, Singapore, Singapore. ⟨10.48550/arXiv.2211.12392⟩

International audience; We introduce continuous $R$-valuations on directed-complete posets (dcpos, for short), as a generalization of continuous valuations in domain theory, by extending values of continuous valuations from reals to so-called Abelian

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08b1b5541f9a38032c6be0c8ea61d819
https://inria.hal.science/hal-04029481/document

On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces

Autor: Goubault-Larrecq, Jean

Publikováno v: Topology Proceedings
Topology Proceedings, 2023, 62, pp.117-131

We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that weak Hausd

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4cbc13de4b691a06e5eda642be2b6f22
http://arxiv.org/abs/2211.10400

Computability of Finite Simplicial Complexes

Autor: Amir, Djamel Eddine, Hoyrup, Mathieu

Publikováno v: ICALP
ICALP, Jul 2022, Paris, France

The topological properties of a set have a strong impact on its computability properties. A striking illustration of this idea is given by spheres and closed manifolds: if a set X is homeomorphic to a sphere or a closed manifold, then any algorithm t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e288611a5a46e7196f32749420846fb