Finite products of limits of direct systems induced by maps
Keywords:complete regularity, the convergent sequence, direct limit, direct system, inclusion direct system, normality, perfect space, pseudo-compact, regularity, sequential convergence, sequential extensor.
AbstractLet Z, H be spaces. In previous work, we introduced the direct (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.
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