Resumen de Finite products of limits of direct systems induced by maps

Ivan Ivansic, Leonard R. Rubin

• Let Z, H be spaces. In previous work, we introduced thedirect (inclusion) system induced by the set of maps between the spaces Z and H. Its direct limit is a subset of Z × H, but its topology is different from the relative topology. We found that many of the spaces constructed from this method are pseudo-compact and Tychonoff. We are going to show herein that these spaces are typically not sequentially compact and we will explore conditions under which a finite product of them will be pseudo-compact.