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On the homotopy equivalence of the spaces of proper and local maps

100%

Bartłomiejczyk P., Nowak-Przygodzki P.

Open Mathematics

2014

tom 12

nr 9

1330-1336

We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.

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 Bartłomiejczyk P.

1 Hattab H.

1 Nowak-Przygodzki P.

1 2017

1 2014

Wyniki wyszukiwania

On the homotopy equivalence of the spaces of proper and local maps

A model of quotient spaces