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Skeletally Dugundji spaces

100%

Kucharski A., Plewik S., Valov V.

Open Mathematics

2013

tom 11

nr 11

1949-1959

We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable inverse spectra, Uspekhi Mat. Nauk, 1976, 31(5), 191–226 (in Russian)] consisting of skeletal maps.

A model of quotient spaces

64%

Hattab H.

Topological Algebra and its Applications

2017

tom 5

nr 1

13-18

Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.

Ograniczanie wyników

1 Open Mathematics

1 Topological Algebra and its Applications

1 Hattab H.

1 Kucharski A.

1 Plewik S.

1 Valov V.

1 2017

1 2013

Wyniki wyszukiwania

Skeletally Dugundji spaces

A model of quotient spaces