The original Brouwerian counter examples were algorithmic in nature; after the introduction of choice sequences, Brouwer devised a version which did not depend on algorithms. This is the origin of the creating subject technique. The method allowed stronger refutations of classical principles. Here it is used to show that negative dense subsets of the continuum are indecomposable.

The purpose of this paper is an axiomatic study of the interrelations between certain continuity properties. We deal with principles which are equivalent to the statements "every mapping is sequentially nondiscontinuous", "every sequentially nondiscontinuous mapping is sequentially continuous", and "every sequentially continuous mapping is continuous". As corollaries, we show that every mapping of a complete separable space is continuous in constructive recursive mathematics (the Kreisel-Lacombe-Schoenfield-Tsejtin theorem) and in intuitionism.