Geodesic
Injective objects of the category of stratified spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 3-13

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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. 
@article{IVM_2017_2_a0,
     author = {S. M. Ageev and I. A. Zhigulich and Z. N. Silaeva},
     title = {Injective objects of the category of stratified spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--13},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_2_a0/}
}
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S. M. Ageev; I. A. Zhigulich; Z. N. Silaeva. Injective objects of the category of stratified spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 3-13. http://geodesic.mathdoc.fr/item/IVM_2017_2_a0/