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A space $X$ is splittable over a space $Y$ (or splits over $Y$ ) if for every $A \subset X$ there exists a continuous map $f : X \to Y$ with $f^{- 1} f A = A$ . We prove that any $n$ -dimensional polyhedron splits over $𝐑^{2 n}$ but not necessarily over $𝐑^{2 n - 2}$ . It is established that if a metrizable compact $X$ splits over $𝐑^{n}$ , then $dim X \leq n$ . An example of $n$ -dimensional compact space which does not split over $𝐑^{2 n}$ is given.

A note on the comparison of topologies.

Kovár, Martin M. (2001)

International Journal of Mathematics and Mathematical Sciences

A note on the topology generated by preopen sets

D. Andrijević, M. Ganster (1987)

Matematički Vesnik

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $b G$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $b G$ such that the remainder $b G ∖ G$ of $G$ belongs to $𝒫$ , then $G$ and $b G ∖ G$ are separable and metrizable, where $𝒫$ is a class of spaces which satisfies the following conditions: (1) if $X \in 𝒫$ , then every compact subset of the space $X$ is a...

A note on transfinite sequences

Norman Howes (1980)

Fundamenta Mathematicae

A Note On Ultrapower Cardinality

Aleksandar Jovanović (1978)

Publications de l'Institut Mathématique

A note on ultrapower cardinality.

A. Jovanovic (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

A note on weakly $θ$ -continuous functions.

Mršević, M., Reilly, I.L. (1989)

International Journal of Mathematics and Mathematical Sciences

A note on weakly $(μ, λ)$ -closed functions

Bishwambhar Roy (2013)

Mathematica Bohemica

In this paper we introduce a new class of functions called weakly $(μ, λ)$ -closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly $(μ, λ)$ -closed functions enable us to facilitate the formulation of certain...

A note on zero-dimensional preimages of compact spaces

Aleksander Błaszczyk (1987)

Acta Universitatis Carolinae. Mathematica et Physica

A note on $α$ -universal spaces

Vilímovský, Jiří (1976)

Seminar Uniform Spaces

A note on $ψ$ -operator.

Modak, Shyampada, Bandyopadhyay, Chhanda (2007)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

A Note Related to a Paper of Noiri

Ilija Kovačević (1984)

Publications de l'Institut Mathématique

A poset of topologies on the set of real numbers

Vitalij A. Chatyrko, Yasunao Hattori (2013)

Commentationes Mathematicae Universitatis Carolinae

On the set $ℝ$ of real numbers we consider a poset $𝒫_{τ} (ℝ)$ (by inclusion) of topologies $τ (A)$ , where $A \subseteq ℝ$ , such that $A_{1} \supseteq A_{2}$ iff $τ (A_{1}) \subseteq τ (A_{2})$ . The poset has the minimal element $τ (ℝ)$ , the Euclidean topology, and the maximal element $τ (\emptyset)$ , the Sorgenfrey topology. We are interested when two topologies $τ_{1}$ and $τ_{2}$ (especially, for $τ_{2} = τ (\emptyset)$ ) from the poset define homeomorphic spaces $(ℝ, τ_{1})$ and $(ℝ, τ_{2})$ . In particular, we prove that for a closed subset $A$ of $ℝ$ the space $(ℝ, τ (A))$ is homeomorphic to the Sorgenfrey line $(ℝ, τ (\emptyset))$ iff $A$ is countable. We study also common properties...

A Priestley view of spatialization of frames

A. Pultr, J. Sichler (2000)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

A pseudocompact space with Kelley's property has a strictly positive measure

N. Kalamidas (1997)

Rendiconti del Seminario Matematico della Università di Padova

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