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Injective objects in the category of stratified spaces

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Abstract

The paper deals with the category of stratified spaces. For this category we establish the existence of the absolute extensors and study their connection with the absolute extensors in the category of filtered spaces. To this end, we introduce and investigate the absolute extensors reflecting the properties of both the filtered category and the stratified category. We determine the contractibility property as well as the local contractibility property for the stratified absolute extensors. It is shown that the family of strata for a stratified absolute neighbourhood extensor is equicontinuously locally extendable.

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Authors and Affiliations

  1. Belarusian State University, pr. Nezavisimosti 4, Minsk, 220030, Republic of Belarus

    S. M. Ageev & I. A. Zhigulich

  2. A. S. Pushkin Brest State University, bulv. Kosmonavtov 21, Brest, 224016, Republic of Belarus

    Z. N. Silaeva

Authors
  1. S. M. Ageev
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  2. I. A. Zhigulich
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  3. Z. N. Silaeva
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Corresponding author

Correspondence to S. M. Ageev.

Additional information

Original Russian Text ©S.M. Ageev, I.A. Zhigulich, Z.N. Silaeva, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 2, pp. 3–13.

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Ageev, S.M., Zhigulich, I.A. & Silaeva, Z.N. Injective objects in the category of stratified spaces. Russ Math. 61, 1–9 (2017). https://doi.org/10.3103/S1066369X17020013

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  • DOI: https://doi.org/10.3103/S1066369X17020013

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