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, or the surface area of two-dimensional grid continua are introduced and discussed.
Description:
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