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

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