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Computability of Generalized Graphs

Author

Listed:
  • Zvonko Iljazović

    (Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
    These authors contributed equally to this work.)

  • Matea Jelić

    (Faculty of Civil Engineering, Architecture and Geodesy, University of Split, 21000 Split, Croatia
    These authors contributed equally to this work.)

Abstract

We investigate conditions under which a semicomputable set is computable. In particular, we study topological pairs ( A , B ) which have a computable type, which means that in any computable topological space, a semicomputable set S is computable if there exists a semicomputable set T such that ( S , T ) is homeomorphic to ( A , B ) . It is known that ( G , E ) has a computable type if G is a topological graph and E is the set of all its endpoints. Furthermore, the same holds if G is a so-called chainable graph. We generalize the notion of a chainable graph and prove that the same result holds for a larger class of spaces.

Suggested Citation

  • Zvonko Iljazović & Matea Jelić, 2024. "Computability of Generalized Graphs," Mathematics, MDPI, vol. 12(22), pages 1-28, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3468-:d:1515453
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