All Parovichenko spaces may be soft-Parovichenko

Journal article (2022)

Authors

Alan Dow University of North Carolina at Charlotte

K.P. Hart Analysis -

Research Group

Analysis () (TU Delft)

Compactification Continuum Hypothesis Soft compactification Parovichenko space

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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

It is shown that, assuming the Continuum Hypothesis, every compact Hausdorff space of weight at most c is a remainder in a soft compactification of N.

We also exhibit an example of a compact space of weight aleph_1 ---hence a remainder in some compactification of N ---for which it is consistent that is not the remainder in a softcompactification of N.

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