Emilia Haluskova – On discrete properties of real continuous monotone functions

Mathematical Institute SAS, Kosice, Slovakia
Let I be an interval of real numbers and h be a function from I into I such that h is monotone and continuous. The component partition of the algebra (I,h) will be given. There are exactly 4 non-isomorphic connected monounary algebras such that they can be components of (I,h). We will show that only 10 cases are possible for (I,h).