A solution to the L space problem
By Justin Tatch Moore. 2005
111 citations recorded by the source corpus.
In this paper I will construct a non-separable hereditarily Lindelof space (L space) without any additional axiomatic assumptions. I will also show that there is a function f from [omega_1]^2 to omega_1 such that if A,B, subsets of omega_1, are uncountable and x omega_1, then there are a < b in A and B respectively with f(a,b) = x. Previously it was unknown whether such a function existed even if omega_1 was replaced by 2. Finally, I will prove that there is no basis for the uncountable regular Hausdorff spaces of cardinality aleph_1. Each of these results gives a strong refutation of a well known and longstanding conjecture. The results all stem from the analysis of oscillations of coherent sequences {e_i : i < omega_1} of finite-to-one functions. I expect that the methods presented will have other applications as well.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/494eed7cae3118382b5524732e669d0fcc7c1387
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Citations in the corpus
- Lindelöf indestructibility, topological games and selection principles (2009, methodology): “In [35] Moore solved the famous L-space problem by constructing a non-separable zero-dimensional hereditarily Lindelöf subspace X of the ω1-power of the unit circle.”
- A survey of D-spaces (2010, background): “Scheepers and Tall [61] show that adding א1 Cohen reals to a model makes any ground model Lindelöf space Rothberger (hence D), and that Moore’s ZFC L-space [46] is Rothberger.”