CCS-normal and B-normal spaces

A space [Formula: see text] is called [Formula: see text]-normal (respectively, [Formula: see text]-normal) if there exist a normal space [Formula: see text] and a bijection [Formula: see text] such that [Formula: see text] is a homeomorphism for any cellular-compact (resp. [Formula: see text]-bounded) subset [Formula: see text] of [Formula: see text]. We investigate the relationship between [Formula: see text]-normal space and [Formula: see text]-normal space and also study the basic topological properties of [Formula: see text]-normal and [Formula: see text]-normal space. In the course of this study, we prove the submetrizable spaces are [Formula: see text]-normal which answers affirmatively, a question raised earlier, and yields a very simple proof of the fact [Formula: see text]-space and Niemytzki plane are [Formula: see text]-normal, proved quite painstakingly in Applied General Topology, Vol 21, No. 1 (2020). A large class of spaces that are [Formula: see text]-normal is given here.