Subspaces of monotonically normal compacta

Details Subspaces of monotonically normal compacta Subspaces of monotonically normal compacta

2012-02-17

arxiv.org/abs/1202.4018v1

Mathematics

General Topology

Scientific paper

We analyze the structure of topological spaces having monotonically normal compactifications. By results of Gruenhage and Eisworth, it is immediate that under PFA, the class M of uncountable subspaces of monotonically normal compacta has a 3-element basis. We show that the same holds under MA_{aleph_1}. Variants of the "canonical" basis are exhibited, further elucidating the structure of M. Our main tools are Nikiel's conjecture and a combinatorial lemma we establish for continuous images of compact ordered spaces. Not surprisingly, the double arrow space figures centrally in this study.

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