Diamond-guided Talagrand compacta can fail 2DCP and local homogeneity while remaining Grothendieck Efimov spaces, and no Talagrand compactum admits classical pointwise sequence quotients.
A small Banach space $C(K)$ without nice renormings
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove that consistently $\omega_1<\mathfrak{c}$ and there exists a compact space $K$ whose Banach space $C(K)$ of continuous real-valued functions is Grothendieck, has density $\omega_1$, and admits no renorming which is strictly convex or sequentially Kadets--Klee.
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math.GN 2years
2026 2representative citing papers
The paper proves new theorems on the two-disjoint-copies property for compact spaces, including its absence from all scattered spaces and equivalence to uncountability for metric compact spaces.
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Talagrand compacta, 2DCP, and pointwise quotients
Diamond-guided Talagrand compacta can fail 2DCP and local homogeneity while remaining Grothendieck Efimov spaces, and no Talagrand compactum admits classical pointwise sequence quotients.
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The two-disjoint-copies property for compact spaces, homogeneity and connection with $C_p$-theory
The paper proves new theorems on the two-disjoint-copies property for compact spaces, including its absence from all scattered spaces and equivalence to uncountability for metric compact spaces.