Quotient-universal sequential spaces

R. Sirois-Dumais and Stephen Willard

Vol. 66 (1976), No. 1, 281–284

DOI: 10.2140/pjm.1976.66.281

Abstract

We produce 2^c 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