Continuous digitization in Khalimsky spaces
نویسنده
چکیده
A real-valued function defined on R can sometimes be approximated by a Khalimsky-continuous mapping defined on Z. We elucidate when this can be done and give a construction for the approximation. This approximation can be used to define digital Khalimsky hyperplanes that are topological embeddings of Z into Z. In particular, we consider Khalimsky planes in Z and show that the intersection of two non-parallel Khalimsky planes contains a Khalimsky line.
منابع مشابه
Digital Geometry and Khalimsky Spaces
Melin, E. 2008. Digital Geometry and Khalimsky Spaces (Digital geometri och Khalimskyrum). Uppsala Dissertations in Mathematics 54. vii+47 pp. Uppsala. ISBN 978-91-506-1983-6 Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young. Efim Khalimsky’s topology on the integers, invented in t...
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 150 شماره
صفحات -
تاریخ انتشار 2008