Computability of Generalized Graphs

Zvonko Iljazović and Matea Jelić ()
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Zvonko Iljazović: Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
Matea Jelić: Faculty of Civil Engineering, Architecture and Geodesy, University of Split, 21000 Split, Croatia

Mathematics, 2024, vol. 12, issue 22, 1-28

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.

Keywords: computable topological space; computable type; topological graph; chainable graph; generalized graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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