Naslov
Computability of glued manifolds

Autori
Čelar, Matea ; Iljazović, Zvonko

Izvornik
Journal of logic and computation (0955-792X) 32 (2021), 1; 65-97

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
computable topological space ; computable set ; semicomputable set ; manifold ; adjunction space

Sažetak
We examine conditions under which a semicomputable set in a computable topological space is computable. In particular we examine topological spaces $\Delta $ which have computable type, which means that any semicomputable set homeomorphic to $\Delta $ is computable. It is known that each compact manifold has computable type. In this paper we examine compact manifolds $M$ and $N$ and a space $M\cup _{; ; ; \gamma }; ; ; N$ obtained by gluing $M$ and $N$ together by way of a homeomorphism $\gamma :A\rightarrow B$, where $A$ and $B$ are closed subspaces of $M$ and $N$ respectively. We show that $M\cup _{; ; ; \gamma }; ; ; N$ in general need not have computable type. We prove that $M\cup _{; ; ; \gamma }; ; ; N$ has computable type under the additional assumption that $A$ and $B$ are contained in regular submanifolds of $M$ and $N$. We also show that the same holds for a space obtained by gluing finitely many manifolds, but not for infinitely many.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo

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