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


  • R. B. Beshimov National University of Uzbekistan
  • Dimitrios N. Georgiou University of Patras
  • R. M. Zhuraev National University of Uzbekistan



G-permutation degree space, uniform space, uniform connectedness, index boundedness of uniform space, uniform continuity


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.


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Author Biography

Dimitrios N. Georgiou, University of Patras

Department of mathematics


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How to Cite

R. B. Beshimov, D. N. Georgiou, and R. M. Zhuraev, “Index boundedness and uniform connectedness of space of the G-permutation degree”, Appl. Gen. Topol., vol. 22, no. 2, pp. 447–459, Oct. 2021.