Finite products of limits of direct systems induced by maps

Ivan Ivansic

Croatia

University of Zagreb

Leonard R. Rubin

United States

University of Oklahoma

Submitted: 2014-12-11

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Accepted: 2015-03-20

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Published: 2015-10-01

DOI: https://doi.org/10.4995/agt.2015.3449
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Keywords:

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

Supporting agencies:

This research was not funded

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.
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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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