Can the spatially closed Friedmann-Robertson-Walker universe (FRW) look like the flat or the open ones? In this paper the topological defects called textures, which are nonlocalized and stable solutions of classical equations of motion on a spatial manifold with compact dimensions, have been the effect responsible for the simulation of flat or open FRW universes from the originally closed one. The paper treats the case of gauge textures in two examples. In the first one a complex spinor field is considered, which leads to a nonphysical texture. In the second one, the entire O(4) symmetry is gauged. A non- abelian magnetic field is found everywhere in the universe, however it is wound away through spatial rotations and unbroken isorotations. The energy density redshifts with \(a^{-4}\) and so the effects causing the closed FRW universe to look like a flat or an open one do not occur any longer. The gauging of textures are shortly analyzed in the paper. The main result is the study of global textures in the \(k=+1\) FRW universe. Further investigations concerning the following questions are pointed out in the article. i) How can astrophysical observations discard certain phenomena connected with these models? ii) What role do fermions play in these models?