Original scientific paper

Computability of sets with attached arcs

Zvonko Iljazović ; Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia
Matea Jelić ; Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia

Abstract

We consider topological spaces $A$ which have computable type, which means that any semicomputable set in a computable topological space which is homeomorphic to $A$ is computable. Moreover, we consider topological pairs $(A,B)$, $B\subseteq A$, which have computable type which means the following: if $S$ and $T$ are semicomputable sets in a computable topological space such that $S$ is homeomorphic to $A$ by a homeomorphism which maps $T$ to $B$, then $S$ is computable. We prove the following: if $B$ has computable type and $A$ is obtained by gluing finitely
many arcs to $B$ along their endpoints, then $(A,B)$ has computable type. We also examine spaces obtained in the same way by gluing chainable continua.

Keywords

computable topological space, semicomputable set, computable set, computable type, chainable continuum

Hrčak ID:

315317

URI

https://hrcak.srce.hr/315317

Publication date:

19.3.2024.

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