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Let      X X       be a Tychonoff space. It was proved by Terada that if the cellularity of      X X       is not Ulam-measurable, then no point of      υ  X ∖  X \upsilon X\backslash X       is a remote point of      X X      . In this paper we generalize this result by proving that if      X X       is barely      α  \alpha      -compact, then no point in      β  α  X ∖  X {\beta _\alpha }X\backslash X       is an      α  \alpha      -exotic point of      X X      . This implies, in particular, that if no cellular family in      X X       has a      α  \alpha      -measurable cardinality, then no point of      β  α  X ∖  X {\beta _\alpha }X\backslash X       is a remote point of      X X      ; the Terada theorem then follows as a corollary when      α  = ω  1 \alpha = {\omega _1}      .

On barely 𝛼-compact spaces and remote points in 𝛽_{𝛼}𝑋_{𝑋}