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Inserting measurable functions precisely

Javier Gutiérrez García;  Tomasz Kubiak — 2014

Czechoslovak Mathematical Journal

A family of subsets of a set is called a σ -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A σ -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect σ -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a σ -topological version of Katětov-Tong...

Topological calculus for separating points from closed sets by maps

Javier Gutiérrez García;  Tomasz Kubiak — 2012

Czechoslovak Mathematical Journal

Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.

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