This article is cited in 2 papers

Injective objects of the category of stratified spaces

S. M. Ageev^a, I. A. Zhigulich^a, Z. N. Silaeva<sup>b

a</sup> Belarusian State University, 4 Nezavisimosti Ave., Minsk, 220030 Republic of Belarus
^b A.S. Pushkin Brest State University, 21 Kosmonavtov blvd., Brest, 224016 Republic of Belarus

Abstract: We investigate the category of stratified spaces. We establish the existence of absolute extensors of the category of stratified spaces and determine its correlation with absolute extensors of the category of filtered spaces. For this purpose we introduce and investigate absolute extensors including properties of the filtered category and the stratified category. We determine the properties of contractibility and local contractibility of stratified absolute extensors. It is shown the family of strata of stratified absolute extensors has the property of equicontinuous local extensibility.

Keywords: spaces with filtration, filtered and stratified maps, absolute extensors and universal spaces of the category of stratified spaces.

UDC: 515.124

Received: 27.07.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:2, 1–9

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