In this paper, new definitions of chaos, exact chaos,
mixing chaos, and weak mixing chaos called θ-chaos, θ exact
chaos, θ-mixing chaos are introduced and
extended to topological spaces. Our purpose is to investigate other types of transitivity,
chaos and mixing, because when we confirm not existence of θ-transitivity we confirm not existence of other types of transitive
functions and its absence cannot find other types of transitivity. So the author
must confirm the existence of this type of transitivity. We have proved that these
chaotic definitions are all preserved under θ r-conjugation.