On the Computability of Rectifiable Simple Curve (Extended Abstract)

Rettinger, Robert; Zheng, Xizhong

doi:10.4230/OASIcs.CCA.2009.2273

Document

On the Computability of Rectifiable Simple Curve (Extended Abstract)

Authors Robert Rettinger, Xizhong Zheng

Part of: Volume: 6th International Conference on Computability and Complexity in Analysis (CCA'09) (CCA 2009)
Part of: Series: Open Access Series in Informatics (OASIcs)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2009-11-25

PDF

File

PDF

OASIcs.CCA.2009.2273.pdf

Filesize: 287 kB
11 pages

Document Identifiers

DOI: 10.4230/OASIcs.CCA.2009.2273
URN: urn:nbn:de:0030-drops-22736

Subject Classification

Keywords

Computable curve
simple curve
rectifiable curve
point separability

Metrics

Access Statistics
Total Accesses (updated on a weekly basis)

0

PDF Downloads

0

Metadata Views

Abstract

In mathematics curves are defined as the images of continuous real functions defined on closed intervals and these continuous functions are called parameterizations of the corresponding curves. If only simple curves of finite lengths are considered, then parameterizations can be restricted to the injective continuous functions or even to the continuous length-normalized parameterizations. In addition, a plane curve can also be considered as a connected one-dimensional compact subset of points. By corresponding effectivizations, we will introduce in this paper four versions of computable curves and show that they are all different. More interestingly, we show also that four classes of computable curves cover even different sets of points.

Cite As Get BibTex

Robert Rettinger and Xizhong Zheng. On the Computability of Rectifiable Simple Curve (Extended Abstract). In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 221-232, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/OASIcs.CCA.2009.2273

Author Details

Robert Rettinger

Xizhong Zheng

Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail