Topology of grid continua
Fridrich Sloboda, Bedrich Zat'ko, Reinhard Klette · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
1D and 2D 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 summarized. Particularly, simple 1D gird continua in R2 and in R3, and simple closed 2D grid continua in R3 are emphasized. Concepts for measuring the length of 1D grid continua and the surface area of a 2D grid continuum are introduced and discussed.