Vol. 66, No. 1, 1976

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Quotient-universal sequential spaces

R. Sirois-Dumais and Stephen Willard

Vol. 66 (1976), No. 1, 281–284
Abstract

We produce 2c mutually nonhomeomorphic countable sequential spaces. These are used

(1) to answer in the negative the following question of Michael and Stone [4]: is every regular T1-space which is a quotient of some separable metric space and a continuous image of the space P of irrationals a quotient of P?

(2) to characterize c (with or without the continuum hypothesis) as the smallest cardinal κ with the property that a metric space of cardinality κ exists of which every sequential space of cardinality κ is a quotient.

Mathematical Subject Classification 2000
Primary: 54D55
Milestones
Received: 12 March 1976
Revised: 12 May 1976
Published: 1 September 1976
Authors
R. Sirois-Dumais
Stephen Willard