Abstract
We examine conditions under which, in a computable topological space, a semicomputable set is computable. It is known that in a computable metric space a semicomputable set S is computable if S is a continuum chainable from a to b, where a and b are computable points, or S is a circularly chainable continuum which is not chainable. We prove that this result holds in any computable topological space.
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Zvonko Iljazović was supported in part by the Croatian Science Foundation under Project 7459 CompStruct.
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Čičković, E., Iljazović, Z. & Validžić, L. Chainable and circularly chainable semicomputable sets in computable topological spaces. Arch. Math. Logic 58, 885–897 (2019). https://doi.org/10.1007/s00153-019-00667-w
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DOI: https://doi.org/10.1007/s00153-019-00667-w
Keywords
- Computable topological space
- Computable set
- Semicomputable set
- Chainable continuum
- Circularly chainable continuum