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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

Sažetak

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.

Ključne riječi

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

Hrčak ID:

315317

URI

https://hrcak.srce.hr/315317

Datum izdavanja:

19.3.2024.

Posjeta: 627 *