The index of discontinuous vector fields.
Gottlieb, Daniel H., Samaranayake, Geetha (1995)
The New York Journal of Mathematics [electronic only]
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Gottlieb, Daniel H., Samaranayake, Geetha (1995)
The New York Journal of Mathematics [electronic only]
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Robert Brown (1999)
Banach Center Publications
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The study of fixed points of continuous self-maps of compact manifolds involves geometric topology in a significant way in topological fixed point theory. This survey will discuss some of the questions that have arisen in this study and indicate our present state of knowledge, and ignorance, of the answers to them. We will limit ourselves to the statement of facts, without any indication of proof. Thus the reader will have to consult the references to find out how geometric topology...
Saveliev, Peter (2005)
Fixed Point Theory and Applications [electronic only]
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Brown, Robert F. (2006)
Fixed Point Theory and Applications [electronic only]
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Paul Cherenack (1995)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Marian Mrozek, James Reineck, Roman Srzednicki (1999)
Banach Center Publications
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In this note we present the main ideas of the theory of the Conley index over a base space introduced in the papers [7, 8]. The theory arised as an attempt to solve two questions concerning the classical Conley index. In the definition of the index, the exit set of an isolating neighborhood is collapsed to a point. Some information is lost on this collapse. In particular, topological information about how a set sits in the phase space is lost. The first question addressed is how to retain...
Marcio Fenille (2014)
Open Mathematics
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We construct an epsilon coincidence theory which generalizes, in some aspect, the epsilon fixed point theory proposed by Robert Brown in 2006. Given two maps f, g: X → Y from a well-behaved topological space into a metric space, we define µ ∈(f, g) to be the minimum number of coincidence points of any maps f 1 and g 1 such that f 1 is ∈ 1-homotopic to f, g 1 is ∈ 2-homotopic to g and ∈ 1 + ∈ 2 < ∈. We prove that if Y is a closed Riemannian manifold, then it is possible to attain µ...
Brooks, Robin (2004)
Fixed Point Theory and Applications [electronic only]
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Soderlund, Christina L. (2006)
Fixed Point Theory and Applications [electronic only]
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C. Wall (1967)
Fundamenta Mathematicae
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R. Dobreńko, Z. Kucharski (1990)
Fundamenta Mathematicae
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