Primitive shifts on ψ-spaces.
Gutek, A. Moshokoa, S.P. Rajagopalan, M. Sundaresan, K.
Gutek, A.
Moshokoa, S.P.
Rajagopalan, M.
Sundaresan, K.
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Abstract
Let D be a countable discrete space and let p ∈ D. For any primitive shift σ : D → D \ {p} there are 2c σ-invariant maximal almost disjoint families on D. This implies that there are 2c pairwise non-homeomorphic Ψ∗ spaces admitting primitive shifts. Under a = c there exists a maximal almost disjoint family F on a countable discrete space D such that the spaces Ψ (F) and Ψ∗(F) admit no primitive shift.
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Date
2011-01-01
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Publisher
Elsevier
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Keywords
Isometric shift, Primitive shift, Maximal almost disjoint family, Ψ-space, Ψ∗-space