0000000000802671

AUTHOR

M. M. Marsh

showing 2 related works from this author

InternallyK-like spaces and internal inverse limits

2014

Abstract We establish equivalences between compacta that admit mappings that limit to the identity, and compacta that are inverse limits of the images under these maps. Our results have relationships to Mardesic and Segalʼs equivalence between polyhedra-like compacta and inverse limits of polyhedra, to the Anderson–Choquet Embedding Theorem, to approximative absolute neighborhood retracts, and to continua that are approximated from within as defined by C.A. Eberhart and J.B. Fugate.

PolyhedronPure mathematicsMathematical analysisInverseEmbeddingGeometry and TopologyEquivalence (formal languages)MathematicsTopology and its Applications
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Internal inverse limits and retractions

2015

We establish equivalences between compacta that admit a sequence of retractions that converge uniformly to the identity map and compacta that are inverse limits on subcompacta with retractions for bonding maps. We give partial answers to questions of Charatonik and Prajs, and of Krasinkiewicz. Our results are related to and use results from another paper of the authors \cite{mp}.

Discrete mathematicsSequenceGeneral Mathematics54A20Inverse$r$-maps54F6554C15retractions54F15CalculusIdentity functionInternal inverse limitMathematics
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