Complete Regularity

Jorge Picado and Aleš Pultr
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Jorge Picado: University of Coimbra, CMUC, Department of Mathematics
Aleš Pultr: Charles University, Department of Applied Mathematics

Chapter Chapter VI in Separation in Point-Free Topology, 2021, pp 107-136 from Springer

Abstract: Abstract In this chapter we will discuss complete regularity. It is very naturally conservatively extended and hence the basic facts will be similar to those in classical spaces. In some respects, however, the point-free approach brings better results. Some of the facts are just more transparent, but there are also results that are entirely out of the classical scope. In particular, in the category of (completely regular) spaces there is no Lindelöf reflection; in the localic extension there is, and quite an interesting one.

Date: 2021
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DOI: 10.1007/978-3-030-53479-0_6

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