J. Roberts and the author have recently shown that, under the Continuum Hypothesis, the Banach space is primary. Since this space is isometrically isomorphic to the space of continuous scalar functions on , it is quite natural to consider the question of primariness also for the spaces of continuous vector functions on . The present paper contains some partial results in that direction. In particular, from our results it follows that is primary for any infinite metrizable (without assuming the CH).

1980 Mathematics Subject Classification (1985 revision): 46E15, 46E25.