2 problems

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The compactness–sequential compactness conjecture for first countable perfectly normal spaces
Compactness–sequential compactness conjecture. For first countable perfectly normal spaces, compactness and sequential compactness should coincide.
Conjectureopencompactness general-topology sequential-spacesarXiv posted 2 days ago
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Negative conjecture for sequentiality and Fréchet–Urysohn properties of $C_p(X,\mathbf{2})$
Negative conjecture. Both answers are negative: there are such spaces $X$ for which $C_p(X,\mathbf{2})$ is not Fréchet–Urysohn and $C_p(X,\mathbf{2})^\omega$ is not sequential.
Conjectureopenfunction-spaces general-topology sequential-spacesarXiv posted 2 days ago

The compactness–sequential compactness conjecture for first countable perfectly normal spaces