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Bad Wadge-like reducibilities on the Baire space

Luca Motto Ros (2014)

Fundamenta Mathematicae

We consider various collections of functions from the Baire space ω ω into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on ω ω (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...

Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

We characterize Baire-like spaces Cc(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

Baire-one mappings contained in a usco map

Ondřej F. K. Kalenda (2007)

Commentationes Mathematicae Universitatis Carolinae

We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in d is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.

Basic constructions in rational homotopy theory of function spaces

Urtzi Buijs, Aniceto Murillo (2006)

Annales de l’institut Fourier

Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.

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