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## Main Question or Discussion Point

I'm fairly certain that the following statement requires the assumption that the topology is first countable, can someone verify this?

If for every sequence x_n → x, E contains all but finitely many x_n, than x is in the interior of E.

Thanks.

If for every sequence x_n → x, E contains all but finitely many x_n, than x is in the interior of E.

Thanks.