Index boundedness and uniform connectedness of space of the G-permutation degree

• Beshimov, R. B. ^[1] ; Georgiou, Dimitrios N. ^[2] ; Zhuraev, R. M. ^[1]
  1. [1] National University of Uzbekistan

     National University of Uzbekistan

     Uzbekistán

     
  2. [2] University of Patras

     University of Patras

     Dimos Patras, Grecia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 447-459
• Idioma: inglés
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• Resumen

  • In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.