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Notes on monotone Lindelöf property

Ai-Jun Xu, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.

Notes on Retracts of Coset Spaces

J. van Mill, G. J. Ridderbos (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of...

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.

On a class of real normed lattices

C. Alegre, Jesús Ferrer, Valentín Gregori (1998)

Czechoslovak Mathematical Journal

We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that E is a quasi-Baire space iff ( E , T ( 𝒰 ) , T ( 𝒰 - 1 ) ) , is a pairwise Baire bitopological space, where 𝒰 , is a quasi-uniformity that determines, in L . Nachbin’s sense, the topological ordered space E .

On a compactification of the homeomorphism group of the pseudo-arc

Kazuhiro Kawamura (1991)

Colloquium Mathematicae

A continuum means a compact connected metric space. For a continuum X, H(X) denotes the space of all homeomorphisms of X with the compact-open topology. It is well known that H(X) is a completely metrizable, separable topological group. J. Kennedy [8] considered a compactification of H(X) and studied its properties when X has various types of homogeneity. In this paper we are concerned with the compactification G P of the homeomorphism group of the pseudo-arc P, which is obtained by the method of...

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