<title>Topology of grid continua</title>

Abstract

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 R<SUP>2</SUP> and R<SUP>3</SUP> are summarized. Particularly, simple 1D gird continua in R<SUP>2</SUP> and in R<SUP>3</SUP>, and simple closed 2D grid continua in R<SUP>3</SUP> are emphasized. Concepts for measuring the length of 1D grid continua and the surface area of a 2D grid continuum are introduced and discussed.