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Extreme topological measures

S. V. Butler (2006)

Fundamenta Mathematicae

It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.

Generalized analytic spaces, completeness and fragmentability

Petr Holický (2001)

Czechoslovak Mathematical Journal

Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.

Hyperspace selections avoiding points

Valentin Gutev (2022)

Commentationes Mathematicae Universitatis Carolinae

We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic...

If it looks and smells like the reals...

Franklin Tall (2000)

Fundamenta Mathematicae

Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define X M to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if X M is homeomorphic to ℝ, then X = X M . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.

Inverse limits of tentlike maps on trees

Stewart Baldwin (2010)

Fundamenta Mathematicae

We investigate generalizations of Ingram's Conjecture involving maps on trees. We show that for a class of tentlike maps on the k-star with periodic critical orbit, different maps in the class have distinct inverse limit spaces. We do this by showing that such maps satisfy the conclusion of the Pseudo-isotopy Conjecture, i.e., if h is a homeomorphism of the inverse limit space, then there is an integer N such that h and σ̂^N switch composants in the same way, where σ̂ is the standard shift map of...

Irreducibility of inverse limits on intervals

David Ryden (2000)

Fundamenta Mathematicae

A procedure for obtaining points of irreducibility for an inverse limit on intervals is developed. In connection with this, the following are included. A semiatriodic continuum is defined to be a continuum that contains no triod with interior. Characterizations of semiatriodic and unicoherent continua are given, as well as necessary and sufficient conditions for a subcontinuum of a semiatriodic and unicoherent continuum M to lie within the interior of a proper subcontinuum of M.

Isolated points and redundancy

P. Alirio J. Peña, Jorge E. Vielma (2011)

Commentationes Mathematicae Universitatis Carolinae

We describe the isolated points of an arbitrary topological space ( X , τ ) . If the τ -specialization pre-order on X has enough maximal elements, then a point x ∈ X is an isolated point in ( X , τ ) if and only if x is both an isolated point in the subspaces of τ -kerneled points of X and in the τ -closure of { x } (a special case of this result is proved in Mehrvarz A.A., Samei K., On commutative Gelfand rings, J. Sci. Islam. Repub. Iran 10 (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime...

L J -spaces

Yin-Zhu Gao (2007)

Czechoslovak Mathematical Journal

In this paper L J -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and J -spaces researched by E. Michael. A space X is called an L J -space if, whenever { A , B } is a closed cover of X with A ∩ B compact, then A or B is Lindelöf. Semi-strong L J -spaces and strong L J -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.

On a characterization of the unit interval in terms of clones

Artur Barkhudaryan (1999)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

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