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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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Detalles Bibliográficos
Autores principales: Dow, A, Hart, K P
Lenguaje:eng
Publicado: 1998
Materias:
Acceso en línea:http://cds.cern.ch/record/356413
Descripción
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.