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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...
Autores principales: | , |
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Lenguaje: | eng |
Publicado: |
1998
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Materias: | |
Acceso en línea: | http://cds.cern.ch/record/356413 |
Sumario: | 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. |
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