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Completeness properties of function rings in pointfree topology

Bernhard Banaschewski, Sung Sa Hong (2003)

Commentationes Mathematicae Universitatis Carolinae

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

Completion theorem for uniform entropy

Takashi Kimura (1998)

Commentationes Mathematicae Universitatis Carolinae

Modifying Bowen's entropy, we introduce a new uniform entropy. We prove that the completion theorem for uniform entropy holds in the class of all metric spaces. However, the completion theorem for Bowen's entropy does not hold in the class of all totally bounded metric spaces.

Complexity of the class of Peano functions

K. Omiljanowski, S. Solecki, J. Zielinski (2000)

Colloquium Mathematicae

We evaluate the descriptive set theoretic complexity of the space of continuous surjections from m to n .

Compositions of simple maps

Jerzy Krzempek (1999)

Fundamenta Mathematicae

A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple.  Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true...

Computing homology.

Kaczynski, Tomasz, Mischaikow, Konstantin, Mrozek, Marian (2003)

Homology, Homotopy and Applications

Concave iteration semigroups of linear set-valued functions

Jolanta Olko (1999)

Annales Polonici Mathematici

We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

Condensations of Cartesian products

Oleg I. Pavlov (1999)

Commentationes Mathematicae Universitatis Carolinae

We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X μ can be condensed onto a normal ( σ -compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserves many properties of X and such that any one-to-one continuous image of M μ , μ ν , contains a closed copy...

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) τ and nw ( K ) τ , then there exists a Tychonoff (regular) topology 𝒯 * 𝒯 such that w ( L , 𝒯 * ) τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

Currently displaying 501 – 520 of 2509