The Hausdorff gap is the well known example of a non-separable, increasingly ordered gap in P(ω)/fin. In this paper new construction of a non-separable gap in P(ω)/fin is presented.
We present, under the Continuum Hypothesis (CH), a construction of an automorphism of P(ω)/fin which maps a Hausdorff gap onto increasingly ordered gap of type (w1, w1) which is not a Hausdorff gap.
We discuss recent results on the connection between properties of a given bounded linear operator of C(ω*) and topological properties of some subset of ω* which the operator determines. A family of closed subsets of ω*, which codes some properties of the operator is defined. An example of application of the method is presented.
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