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We consider various notions of holomorphic extendability of complex valuedfunctions defined on subsets of $\mathbf C^n$, including one-sidedextendability. We show that in the relevant function spaces, these phenomena ofholomorphic extendability are rare in the topological sense, generalizingseveral results of the article "One sided extendability and $p$-continuousanalytic capacities" by E. Bolkas, V. Nestoridis, C. Panagiotis and M.Papadimitrakis, in dimensions $n\ge 2$.

Holomorphic extendability in $\mathbf C^n$ as a rare phenomenon