Finite products of limits of direct systems induced by maps (CROSBI ID 217242)
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Podaci o odgovornosti
Ivanšić, Ivan ; Rubin, Leonaard R.
engleski
Finite products of limits of direct systems induced by maps
Let 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 the product of Z and 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.
complete regularity; the convergent sequence; direct limit; direct system; inclusion direct system; normality; perfect space; pseudo-compact; regularity; sequential convergence; sequential extensor
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