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Displaying similar documents to “Certain questions related to the equivalence of local connectedness and connectedness im kleinen”

Partly dissipative systems in uniformly local spaces

Alexandre N. Carvalho, Tomasz Dlotko (2004)

Colloquium Mathematicae

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We study the existence of attractors for partly dissipative systems in ℝⁿ. For these systems we prove the existence of global attractors with attraction properties and compactness in a slightly weaker topology than the topology of the phase space. We obtain abstract results extending the usual theory to encompass such two-topologies attractors. These results are applied to the FitzHugh-Nagumo equations in ℝⁿ and to Field-Noyes equations in ℝ. Some embeddings between uniformly local spaces...

The Redfield topology on some groups of continuous functions.

Nadal Batle Nicolau, Josep Grané Manlleu (1977)

Stochastica

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The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net...