The present invention relates to textile two- or three-dimensional structures formed from fibers and/or ribbons and swellable materials, the fibers and/or ribbons present in the structure and also the swellable materials each being present in such an amount that the fibers and/or ribbons are encased by the swellable materials and the voids in the structure are, in the swollen state, partially or completely filled by materially bound water and the swellable materials used being aqueous emulsions of (co)polymers of at least one ethylenically unsaturated monomer MON which are applied to the fibers and/or ribbons.