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 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.


complete regularity, the convergent sequence, direct limit, direct system, inclusion direct system, normality, perfect space, pseudo-compact, regularity, sequential convergence, sequential extensor.

Subject classification

54B35; 54C55; 54C20; 54D35; 54F45.

Full Text:



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R. M. Stephenson, Jr., Pseudocompact spaces, Trans. Amer. Math. Soc. 134 (1968), 437-448.

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1. Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes
Leonard R. Rubin
Glasnik Matematicki  vol: 51  issue: 2  first page: 447  year: 2016  
doi: 10.3336/gm.51.2.11

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147