Proceedings of the International Geometry Center

ISSN-print: 2072-9812
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When is the space of semi-additive functionals an absolute (neighbourhood) retract?

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Published Sep 10, 2022
DOI https://doi.org/10.15673/tmgc.v15i2.2020

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Adilbek Atakhanovich Zaitov
Tashkent Institute of Architecture and Civil Engineering, 13, A. Navoi Str., 100011, Tashkent, Uzbekistan. Nukus State Pedagogical Institute, 104, P. Seyitov Str., 230100, Nukus, Karakalpakstan
https://orcid.org/0000-0002-2248-0442
Khamidjon Kurbanov
Academy of the Armed Forces of the Republic of Uzbekistan, 2, Parkent Str., 100023, Tashkent, Uzbekistan
https://orcid.org/0000-0001-9294-8787

Abstract

In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space OSf(X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp(X) is so.

Keywords:
semi-additive functional, absolute (neighbourhood) retract

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How to Cite
Zaitov, A., & Kurbanov, K. (2022). When is the space of semi-additive functionals an absolute (neighbourhood) retract?. Proceedings of the International Geometry Center, 15(2), 87-100. https://doi.org/10.15673/tmgc.v15i2.2020
Issue
Vol 15 No 2 (2022)
Section
Papers

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Author Biographies

Adilbek Atakhanovich Zaitov, Tashkent Institute of Architecture and Civil Engineering, 13, A. Navoi Str., 100011, Tashkent, Uzbekistan. Nukus State Pedagogical Institute, 104, P. Seyitov Str., 230100, Nukus, Karakalpakstan

Tashkent Institute of Architecture and Civil Engineering, 13, A. Navoi Str., 100011, Tashkent, Uzbekistan Nukus State Pedagogical Institute, 104, P. Seyitov Str., 230100, Nukus, Karakalpakstan

Khamidjon Kurbanov, Academy of the Armed Forces of the Republic of Uzbekistan, 2, Parkent Str., 100023, Tashkent, Uzbekistan

Academy of the Armed Forces of the Republic of Uzbekistan, 2, Parkent Str., 100023, Tashkent, Uzbekistan

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