Weak coarse shape equivalences and infinite dimensional Whitehead theorem in coarse shape theory

In this paper, we study the weak coarse shape equivalences. First, we define paradominations and then we give a characterization of them, for uniformly movable pointed continuum spaces. Also, we show that a weak coarse shape equivalence to a pointed movable space is a paradomination. Finally, we prove that a weak coarse shape equivalence F⁎:(X,x)→(Y,y) between pointed continuum spaces is a coarse shape equivalence, if (X,x) and (Y,y) are simultaneously movable according to F⁎.