Constructing Inverse Limits With Upper Semi-continuous Functions
Jonathan Zhou
Pinetree Secondary School
Floor Location : S 178 P

Inverse limits of continuous, one-valued functions on [0; 1] are known to be non-empty, connected, planar, irreducible compacta. However, these properties do not generalize to inverse limits of upper semi-continuous functions. In this paper, we will present conditions under which these properties will or will not hold for upper semi-continuous functions on the metric interval [0; 1]. We will also give examples of inverse limits that cannot be constructed with continuous functions, such as the Cantor set, trees, and the harmonic sequence using upper semi-continuous functions. These examples oer insight to the general techniques one can use to construct more complex topological structures with inverse limits.