by Sloboda, F, Zaťko, B and Klette, R
Abstract:
One-dimensional and two-dimensional continua belong to the basic notions of set-theoretical topology and represent a subfield of the theory of dimensions developed by P. Urysohn and K. Menger. In this paper basic definitions and properties of grid continua in R2 and R3 are summarised. Particularly, simple one-dimensional grid continua in R2 and in R3, and simple closed two-dimensional grid continua in R3 are emphasised. Concepts for measuring the length of one-dimensional grid continua and the surface area of a two-dimensional grid continuum are introduced and discussed.
Reference:
On the topology of grid continua (Sloboda, F, Zaťko, B and Klette, R), In Proceedings of SPIE – The International Society for Optical Engineering, volume 3454, 1998.
Bibtex Entry:
@inproceedings{sloboda1998oncontinua,
author = "Sloboda, F and Zaťko, B and Klette, R",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",
pages = "52--63",
title = "On the topology of grid continua",
volume = "3454",
year = "1998",
abstract = "One-dimensional and two-dimensional continua belong to the basic notions of set-theoretical topology and represent a subfield of the theory of dimensions developed by P. Urysohn and K. Menger. In this paper basic definitions and properties of grid continua in R2 and R3 are summarised. Particularly, simple one-dimensional grid continua in R2 and in R3, and simple closed two-dimensional grid continua in R3 are emphasised. Concepts for measuring the length of one-dimensional grid continua and the surface area of a two-dimensional grid continuum are introduced and discussed.",
doi = "10.1117/12.323274",
issn = "0277-786X",
keyword = "Digital geometry",
keyword = "Minimal polyhedral Jordan surface in R3",
keyword = "One-dimensional grid continua in R2 and R3",
keyword = "Two-dimensional grid continua in R3",
language = "eng",
}