We prove that there is a coincidence index for the inclusion F (x) ∈ Φ(x) when Φ is convex-valued and satisfies certain compactness assumptions on countable sets. For F we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g. F is a Vietoris map). For the special case F = id, the obtained fixed point index is defined if Φ is countably condensing; the a...

Topological maps are vital for fast and accurate localization in large environments. Sparse topological maps can be constructed by partitioning a sequence of images acquired by a robot, according to their appearance. All images in a partition have similar appearance and are represented by a node in a topological map. In this paper, we present a topological mapping framework which makes use of i...

We present a scheme for constructing various Conley indices for locally deened maps. In particular we extend the shape index of Robbin and Salamon to the case of a locally deened map in a locally compact Hausdorr space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity pr...

For a given pair of maps f, g : X → M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg : H(X) → H(M) of degree (−n). We prove a Lefschetztype coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x ∈ X such that f(x) = g(x).