Stratifiability and the μ-space property of function spaces with intermediate topologies
Dedicated to the memory of Prof. Phillip L. Zenor We begin to investigate the stratifiability and the μ space property of intermediate topologies between the toplogies of C_p(X) and C_k(X), for a separable metrizable space X. In particular, for the space P of irrational numbers, we show the following: (1) There is a family K of compact sets of P such that C_K (P) is an M_1-space and the topology of C_K (P) is strictly between that of C_p(X) and that of C_k(P). (2) For any nonzero natural number n, let K be the family of all compact sets with scattered height <n. Then C_K (P) is neither a stratifiable space nor a μ-space. , journal=Topology Proceedings, author=Tamano, Kenichi, year=2021, month=Jun., pages=243–262