wQN spaces and related notions

Abstract

Abstract. We discuss modications of wQN and SSP properties for semicontinuous
functions with values in some special sets of reals and we give the
relations among these notions. We present direct proofs of

$\text{\mbox{\rm wQN}}_{\ast}\to\text{\mbox{\rm wQN}}^{\ast}$ and $\text{\mbox{\rm SSP}}_{\ast}\to\text{\mbox{\rm SSP}}^{\ast}$.