Finite products of limits of direct systems induced by maps

Ivan Ivansic, Leonard R. Rubin

Abstract

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.

Keywords

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.

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References

R. Engelking, General Topology, PWN-Polish Scientific Publishers, Warsaw, 1977.

I. Ivansic and L. Rubin, Pseudo-compactness of direct limits, Topology Appl. 160 (2013), 360-367.

http://dx.doi.org/10.1016/j.topol.2012.11.012

I. Ivansic and L. Rubin, The topology of limits of direct systems induced by maps, Mediterr. J. Math. 11, no. 4 (2014), 1261-1273.

http://dx.doi.org/10.1007/s00009-013-0371-0

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

http://dx.doi.org/10.1090/S0002-9947-1968-0232349-6

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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



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Universitat Politècnica de València

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