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A Universal Continuum of Weight aleph

We prove that every continuum of weight aleph_1 is a continuous image of the Cech-Stone-remainder R^* of the real line. It follows that under CH the remainder of the half line [0,infty) is universal among the continua of weight c. We complement this result by showing that 1) under MA every continuum...

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Autores principales: Dow, A, Hart, K P
Lenguaje:eng
Publicado: 1998
Materias:
Acceso en línea:http://cds.cern.ch/record/356413
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author Dow, A
Hart, K P
author_facet Dow, A
Hart, K P
author_sort Dow, A
collection CERN
description We prove that every continuum of weight aleph_1 is a continuous image of the Cech-Stone-remainder R^* of the real line. It follows that under CH the remainder of the half line [0,infty) is universal among the continua of weight c. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R^* 2) in the Cohen model the long segment of length omega_2+1 is not a continuous image of R^*, and 3) PFA implies that I_u is not a continuous image of R^*, whenever u is a c-saturated ultrafilter.
id cern-356413
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1998
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spelling cern-3564132019-09-30T06:29:59Zhttp://cds.cern.ch/record/356413engDow, AHart, K PA Universal Continuum of Weight alephMathematical Physics and MathematicsWe prove that every continuum of weight aleph_1 is a continuous image of the Cech-Stone-remainder R^* of the real line. It follows that under CH the remainder of the half line [0,infty) is universal among the continua of weight c. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R^* 2) in the Cohen model the long segment of length omega_2+1 is not a continuous image of R^*, and 3) PFA implies that I_u is not a continuous image of R^*, whenever u is a c-saturated ultrafilter.math.GN/9805008oai:cds.cern.ch:3564131998-06-04
spellingShingle Mathematical Physics and Mathematics
Dow, A
Hart, K P
A Universal Continuum of Weight aleph
title A Universal Continuum of Weight aleph
title_full A Universal Continuum of Weight aleph
title_fullStr A Universal Continuum of Weight aleph
title_full_unstemmed A Universal Continuum of Weight aleph
title_short A Universal Continuum of Weight aleph
title_sort universal continuum of weight aleph
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/356413
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