Displaying similar documents to “Local extension of maps.”

Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza, Angel Tamariz-Mascarúa, Humberto Villegas-Rodríguez (2013)

Commentationes Mathematicae Universitatis Carolinae

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Given a Tychonoff space X , a base α for an ideal on X is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on α converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

Coronas of ultrametric spaces

Igor V. Protasov (2011)

Commentationes Mathematicae Universitatis Carolinae

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We show that, under CH, the corona of a countable ultrametric space is homeomorphic to ω * . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.

On absolutely submetrizable spaces

Raushan Z. Buzyakova (2006)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums. ...

On van Douwen spaces and retracts of β

Alan S. Dow (2007)

Mathematica Bohemica

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Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of β . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of β expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).