In this small text the basic theory of the continuum, including the
elements of metric space theory and continuity is developed within
the system of intuitionistic mathematics in the sense of L.E.J.
Brouwer and H. Weyl. The main features are proofs of the famous
theorems of Brouwer concerning the continuity of all functions that
are defined on "whole" intervals, the uniform continuity of all
functions that are defined on compact intervals, and the uniform
convergence of all pointwise converging sequences of functions
defined on compact intervals. The constructive approach is
interesting both in itself and as a contrast to, for example, the
formal axiomatic one.
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