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Large families of dense pseudocompact subgroups of compact groups

Gerald Itzkowitz, Dmitri Shakhmatov (1995)

Fundamenta Mathematicae

We prove that every nonmetrizable compact connected Abelian group G has a family H of size |G|, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H ∩ H'={0} for distinct H,H' ∈ H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size |G| consisting of proper dense pseudocompact subgroups of G such that each intersection H H'...

Making holes in the cone, suspension and hyperspaces of some continua

José G. Anaya, Enrique Castañeda-Alvarado, Alejandro Fuentes-Montes de Oca, Fernando Orozco-Zitli (2018)

Commentationes Mathematicae Universitatis Carolinae

A connected topological space Z is unicoherent provided that if Z = A ∪ B where A and B are closed connected subsets of Z , then A ∩ B is connected. Let Z be a unicoherent space, we say that z ∈ Z makes a hole in Z if Z - { z } is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.

Mapping theorems on countable tightness and a question of F. Siwiec

Shou Lin, Jinhuang Zhang (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper s s -quotient maps and s s q -spaces are introduced. It is shown that (1) countable tightness is characterized by s s -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) s s q -spaces are characterized as the s s -quotient images of metric spaces; (4) assuming 2 ω < 2 ω 1 , a compact T 2 -space is an s s q -space if and only if every countably compact subset...

Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)

Paul Fabel (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a naturally occuring example of a quotient map such that q × q fails to be a quotient map. With the quotient topology, this example shows π₁(X,p) can fail to be a topological group if X is locally path connected.

On clopen sets in Cartesian products

Raushan Z. Buzyakova (2001)

Commentationes Mathematicae Universitatis Carolinae

The results concern clopen sets in products of topological spaces. It is shown that a clopen subset of the product of two separable metrizable (or locally compact) spaces is not always a union of clopen boxes. It is also proved that any clopen subset of the product of two spaces, one of which is compact, can always be represented as a union of clopen boxes.

Currently displaying 41 – 60 of 113