Topology and its Applications 122 (2002) 105–133 Applications of another characterization of β N\N Alan Dow a,∗ , Klaas Pieter Hart b,1 a Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Canada M3J 1P3 b Faculty ITS, TU Delft, Postbus 5031, 2600 GA Delft, The Netherlands Received 2 February 2000; received in revised form 27 May 2000 Abstract Stepr¯ ans provided a characterization of β N\N in the ℵ 2 -Cohen model that is much in the spirit of Paroviˇ cenko’s characterization of this space under CH. A variety of the topological results established in the Cohen model can be deduced directly from the properties of β N\N or P (N)/fin that feature in Stepr¯ ans’ result.  2002 Elsevier Science B.V. All rights reserved. AMS classification: Primary 54A35, Secondary 03E35; 06E05; 54D35; 54F65 Keywords: β N; Cohen forcing; Paroviˇ cenko’s theorem; Characterizations Introduction Topological problems that involve the behaviour of families of subsets of the set of nat- ural numbers tend to have (moderately) easy solutions if the Continuum Hypothesis (CH) is assumed. The reason for this is that one’s inductions and recursions last only ℵ 1 steps and that at each intermediate step only countably many previous objects have to be dealt with. An archetypal example is Paroviˇ cenko’s characterization, see [22], of the space N ∗ as the only compact zero-dimensional F -space of weight c without isolated points in which non-empty G δ -sets have non-empty interiors. The proof actually shows that P (N)/fin is the unique atomless Boolean algebra of size c with a certain property R ω and then applies Stone duality to establish uniqueness of N ∗ . It runs as follows: consider two Boolean * Corresponding author. Current address: Department of Mathematics, University of North Carolina at Charlotte, 9201 University City Blvd., Charlotte, NC 28223-0001, USA. The research of the first author was supported in part by the Netherlands Organization for Scientific Research (NWO)—Grant B 61-408 and by NSERC. E-mail addresses: adow@uncc.edu (A. Dow), k.p.hart@its.tudelft.nl (K.P. Hart). URL address: http://aw.twi.tudelft.nl/ hart. 1 The research of the second author was supported in part by the Netherlands Organization for Scientific Research (NWO)—Grant R 61-444. 0166-8641/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII:S0166-8641(01)00138-9