Rad HAZU, Matematičke znanosti, Vol. 21 (2017), 9-20.

COMPUTABILITY OF A WEDGE OF CIRCLES

Zvonko Iljazović and Lucija Validžić

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: zilj@math.hr

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: lucija.validzic@math.hr


Abstract.   We examine conditions under which a semicomputable set in a computable metric space is computable. In particular, we focus on wedge of circles and prove that each semicomputable wedge of circles is computable.

2010 Mathematics Subject Classification.   03D78.

Key words and phrases.   Computable set, semicomputable set, wedge of circles.


Full text (PDF) (free access)

DOI: http://doi.org/10.21857/ygjwrc6j1y


References:

  1. V. Brattka, Plottable real number functions and the computable graph theorem, SIAM J. Comput. 38 (2008), 303-328.
    MathSciNet     CrossRef

  2. V. Brattka and G. Presser, Computability on subsets of metric spaces, Theoret. Comput. Sci. 305 (2003), 43-76.
    MathSciNet     CrossRef

  3. K. Burnik and Z. Iljazović, Computability of 1-manifolds, Log. Methods Comput. Sci. 10 (2014), 2:8, 1-28.
    MathSciNet     CrossRef

  4. S. B. Cooper, Computability Theory, Chapman and Hall/CRC, 2004.
    MathSciNet

  5. Z. Iljazović and L. Validžić, Computable neighbourhoods of points in semicomputable manifolds, Ann. Pure Appl. Logic 168 (2017), 840-859.
    MathSciNet     CrossRef

  6. Z. Iljazović, Compact manifolds with computable boundaries, Log. Methods Comput. Sci. 9 (2013), (4:19), 1-22.
    MathSciNet     CrossRef

  7. Z. Iljazović, Chainable and Circularly Chainable Co-r.e. Sets in Computable Metric Spaces, J.UCS 15 (2009), 1206-1235.
    MathSciNet

  8. Z. Iljazović and B. Pažek, Computable intersection points, preprint.

  9. Z. Iljazović and B. Pažek, Co-c.e. sets with disconnected complements, Theory Comput. Syst. (2017).
    CrossRef

  10. T. Kihara, Incomputability of Simply Connected Planar Continua, Computability 1 (2012), 131-152.
    MathSciNet     CrossRef

  11. J. S. Miller, Effectiveness for Embedded Spheres and Balls, in: Electronic Notes in Theoretical Computer Science, Volume 66, Elsevier, 2002, pp. 127-138.
    CrossRef

  12. J. R. Munkres, Topology, Prentice Hall, 2000.
    MathSciNet

  13. M. B. Pour-El and J. I. Richards, Computability in Analysis and Physics, Springer, Berlin, 1989.
    MathSciNet     CrossRef

  14. E. Specker, Der Satz vom Maximum in der rekursiven Analysis, in: Constructivity in Mathematics (A. Heyting, ed.), North Holland Publishing Co., Amsterdam, 1959, pp. 254-265.
    MathSciNet

  15. K. Weihrauch, Computable Analysis, Springer, Berlin, 2000.
    MathSciNet     CrossRef

  16. K. Weihrauch, Computability on computable metric spaces, Theoret. Comput. Sci. 113 (1993), 191-210.
    MathSciNet     CrossRef


Rad HAZU Home Page