arXiv Open Access 2017

Computable planar paths intersect in a computable point

Klaus Weihrauch

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Abstrak

Consider two paths $f,g:[0;1]\to [0;1]^2$ on the unit square such that $f(0)=(0,0)$, $f(1)=(1,1)$, $g(0)=(0,1)$, $g(1)=(1,0)$, $f(0;1)\subseteq (0;1)^2$ and $g(0;1)\subseteq (0;1)^2$. By continuity of $f$ and $g$ there is a point of intersection. We prove that there is a computable point of intersection if the paths are computable.

Topik & Kata Kunci

math.LO

Penulis (1)

Klaus Weihrauch

Format Sitasi

APA MLA BibTeX

Weihrauch, K. (2017). Computable planar paths intersect in a computable point. https://arxiv.org/abs/1708.07460

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓