2 problems

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The product characterization of countable dense homogeneity for filters
Product characterization conjecture. The following conditions are equivalent:
Conjectureopenfilters set-theory topological-homogeneityarXiv posted 2 days ago
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Hoehn's small-case conjecture for the square
Hoehn's small-case conjecture. The statement $(\ast)_2$ is true.
Conjectureopenfunction-spaces homeomorphism-groups topological-homogeneityarXiv posted 2 days ago

The product characterization of countable dense homogeneity for filters