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Pointwise convergence fails to be strict

Ján Borsík, Roman Frič (1998)

Czechoslovak Mathematical Journal

It is known that the ring B ( ℝ ) of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring C ( ℝ ) of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of C ( ℝ ) . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of C ( ℝ ) which differs from B ( ℝ ) .

Probabilistic approach spaces

Gunther Jäger (2017)

Mathematica Bohemica

We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to...

Productively Fréchet spaces

Francis Jordan, Frédéric Mynard (2004)

Czechoslovak Mathematical Journal

We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also Fréchet.

Products of topological spaces and families of filters

Paolo Lipparini (2023)

Commentationes Mathematicae Universitatis Carolinae

We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by ≤ ω 1 factors are Lindelöf. Parallel results are obtained for final ω n -compactness, [ λ , μ ] -compactness, the Menger and the Rothberger properties.

Pseudouniform topologies on C ( X ) given by ideals

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

Commentationes Mathematicae Universitatis Carolinae

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.

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