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Hausdorff topology and uniform convergence topology in spaces of continuous functions

Umberto Artico, Giuliano Marconi (1995)

Commentationes Mathematicae Universitatis Carolinae

The local coincidence of the Hausdorff topology and the uniform convergence topology on the hyperspace consisting of closed graphs of multivalued (or continuous) functions is related to the existence of continuous functions which fail to be uniformly continuous. The problem of the local coincidence of these topologies on $C (X, Y)$ is investigated for some classes of spaces: topological groups, zero-dimensional spaces, metric manifolds.

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces $X$ which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii $α_{1}$ spaces, for which every sheaf at a point can be amalgamated in a natural way. Let $C_{p} (X)$ denote the space of continuous real-valued functions on $X$ with the topology of pointwise convergence. Our main result...

We investigate how the Lindelöf property of the function space $C_{p} (X, Y)$ is influenced by slight changes in $X$ and/or $Y$ .

Displaying 1 – 7 of 7

Hausdorff topology and uniform convergence topology in spaces of continuous functions

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Hereditary m-separability and the hereditary m-Lindelöf property in product spaces and function spaces

Hereditary $κ$ -separability and the hereditary $κ$ -Lindelöf property in function spaces

Homology of Function Spaces.

Homotopy Decompositions of Equivariant Function Spaces. II. Function Spaces of Equivariantly Triangulated Spaces.

How sensitive is $C_{p} (X, Y)$ to changes in $X$ and/or $Y$ ?

Currently displaying 1 – 7 of 7

Displaying 1 – 7 of 7

Hausdorff topology and uniform convergence topology in spaces of continuous functions

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Hereditary m-separability and the hereditary m-Lindelöf property in product spaces and function spaces

Hereditary κ -separability and the hereditary κ -Lindelöf property in function spaces

Homology of Function Spaces.

Homotopy Decompositions of Equivariant Function Spaces. II. Function Spaces of Equivariantly Triangulated Spaces.

How sensitive is C p ( X , Y ) to changes in X and/or Y ?

Currently displaying 1 – 7 of 7

Hereditary $κ$ -separability and the hereditary $κ$ -Lindelöf property in function spaces

How sensitive is $C_{p} (X, Y)$ to changes in $X$ and/or $Y$ ?