C^*-Embedded Dense Subsets of z-Neighborhood-Sublinear Spaces Are P-Embedded - Hirata, Yasushi; Kemoto, Nobuyuki; Ohta, Haruto (Topology Proceedings, 2023)
We define a concept of z-neighborhood-sublinear space and point out that - every first-countable Tychonoff space and every generalized ordered space is z-neighborhood-sublinear, and - subspaces and finite products of z-neighborhood-sublinear spaces are z-neighborhood-sublinear. As a main theorem, we prove that every C^*-embedded dense subset of a z-neighborhood-sublinear space is P-embedded. The first author and Yukinobu Yajima, in [C^*.-embedding implies P-embedding in products of ordinals, Topology and Appl., 231 (2017), pp. 251-265], prove that for all subspaces A and B of an ordinal, if a closed subset F of A × B is C^*-embedded in A × B, then F is P-embedded in A × B. We can remove closedness from the assumption by applying the main theorem.