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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'...

Linking the closure and orthogonality properties of perfect morphisms in a category

David Holgate (1998)

Commentationes Mathematicae Universitatis Carolinae

We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.

Local connectivity, open homogeneity and hyperspaces.

J. J. Charatonik (1993)

Revista Matemática de la Universidad Complutense de Madrid

In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains...

Local extension of maps.

Barr, Michael, Kennison, John F., Raphael, R. (2009)

The New York Journal of Mathematics [electronic only]

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