Compact-range Vietoris powers: from $\omega+1$ to all countable ordinals above $\omega$

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This event attributed to Lucas Alves de Almeida

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First, On the Vietoris Power of a Convergent Sequence settles the highlighted case $\alpha=\omega+1$: the space is second-countable and Lindelöf, but not $\sigma$-compact. Compact families of surjections have finite bounds on where each isolated value occurs; a delayed diagonal defeats every countable compact cover. The stronger manuscript proves, for every $\omega<\alpha<\omega_1$, second countability and Lindelöfness, together with failure of both $\sigma$-compactness and the Menger property. It combines a countable-base argument, transfer through a closed copy of $[0,\omega]$, and a direct fixed-compact-image diagonal. Explicit increasing open covers and the same diagonal defeat all finite selections, proving non-Mengerness. Thus the original question has a positive answer for Lindelöfness and a negative answer for $\sigma$-compactness. “Proved” refers to this classification theorem. parent of this event

Complete modular Lean recheck: report, logs and hashes (30 September 2026) evidence for this event

First stage: On the Vietoris Power of a Convergent Sequence evidence for this event

Compact-range Vietoris powers: from $\omega+1$ to all countable ordinals above $\omega$ parent of this event

Principal formal theorem: ordinal_full evidence for this event

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Earlier omega+1 repository evidence for this event

VibeMathed record: Compact-range Vietoris powers: from $\omega+1$ to all countable ordinals above $\omega$ evidence for this event

Compact-range Vietoris powers: from $\omega+1$ to all countable ordinals above $\omega$ evidence for this event

Original Question 1, page 11 (arXiv v3) evidence for this event

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