Quotient and pseudo-open images of separable metric spaces

Strong, Paul L.

doi:10.1090/S0002-9939-1972-0300253-7

Quotient and pseudo-open images of separable metric spaces

Author: Paul L. Strong
Journal: Proc. Amer. Math. Soc. 33 (1972), 582-586
MSC: Primary 54B15; Secondary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1972-0300253-7
MathSciNet review: 0300253
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Ernest A. Michael has given a characterization of the regular quotient images of separable metric spaces. His result is generalized here to a characterization of the ${T_1}$ quotient images of separable metric spaces (which are the same as the ${T_1}$ quotient images of second countable spaces). This result is then used to characterize the Hausdorff pseudo-open images of separable metric spaces.

A. V. Arhangel′skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115–162. MR 0227950, DOI https://doi.org/10.1070/RM1966v021n04ABEH004169
S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, DOI https://doi.org/10.4064/fm-57-1-107-115
S. P. Franklin, Spaces in which sequences suffice. II, Fund. Math. 61 (1967), 51–56. MR 222832, DOI https://doi.org/10.4064/fm-61-1-51-56
J. A. Guthrie, A characterization of $\aleph _{0}$-spaces, General Topology and Appl. 1 (1971), no. 2, 105–110. MR 288726
E. Michael, $\aleph _{0}$-spaces, J. Math. Mech. 15 (1966), 983–1002. MR 0206907
Frank Siwiec, Sequence-covering and countably bi-quotient mappings, General Topology and Appl. 1 (1971), no. 2, 143–154. MR 288737