Effectiveness for Embedded Spheres and Balls

  title={Effectiveness for Embedded Spheres and Balls},
  author={Joseph S. Miller},
  journal={Electr. Notes Theor. Comput. Sci.},
We consider arbitrary dimensional spheres and closed balls embedded in Rn as Π1 classes. Such a strong restriction on the topology of a Π1 class has computability theoretic repercussions. Algebraic topology plays a crucial role in our exploration of these consequences; the use of homology chains as computational objects allows us to take algorithmic advantage of the topological structure of our Π1 classes. We show that a sphere embedded as a Π1 class is necessarily located, i.e., the distance… CONTINUE READING
Highly Cited
This paper has 42 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.


Publications citing this paper.
Showing 1-10 of 20 extracted citations


Publications referenced by this paper.
Showing 1-8 of 8 references

Elements of the topology of plane sets of points

M.H.A. Newman
Cambridge University Press, New York, 1961, vii+214 pp. • 1961
View 3 Excerpts
Highly Influenced

Co-c.e. classes in computable analysis and topology

J. S. Miller
Ph.D. dissertation, Cornell University (2002). • 2002
View 1 Excerpt

Computable Analysis

Texts in Theoretical Computer Science. An EATCS Series • 2000
View 1 Excerpt

Computability in analysis and physics

Perspectives in Mathematical Logic • 1989
View 1 Excerpt

Recursive topology in Euclidean space

S. S. Brady
Ph.D. dissertation, Cornell University (1984). • 1984
View 1 Excerpt

A constructive map of the square into itself, which moves every constructive point

V. P. Orevkov
Dokl. Akad. Nauk SSSR • 1963
View 1 Excerpt

Les ensembles récursivement ouverts ou fermés, et leurs applications à l’analyse récursive

D. Lacombe
C. R. Acad. Sci. Paris • 1957
View 1 Excerpt