Topološki seminar Ljubljana-Maribor-Zagreb

Tjaša Lunder (Maribor):

Generalizations of Markov interval functions and inverse limits

We generalize Markov interval functions in two different ways. First, we generalize them to set-valued functions, defined with respect to a finite set of points on the interval; we call these functions generalized Markov interval functions. Second, we generalize them to set valued functions, defined with respect to a countable set of points on the interval; we call them countably Markov interval functions. We show that any two inverse limits with generalized Markov interval bonding functions with the same pattern are homeomorphic. We also show that any two inverse limits with countably Markov interval bonding functions with the same pattern are homeomorphic. Both cases generalize the result from  S. Holte, Inverse limits of Markov interval maps, Topology Appl. 123, 2002, 421--427.

Zvonko Iljazović (Zagreb):

Computability of compact manifolds

If S is a semi-computable subset of Euclidean space, then S
need not be computable. However, under certain topological
assumptions on S, we can conclude that S is computable. In
this talk the following result will be presented: if S is a
compact manifold with boundary and if the boundary of S is
computable, then S is computable.