The Alexandroff Duplicate and its subspaces

Abstract

We study some topological properties of the class of the Alexandroff duplicates and their subspaces. We give a characterization of metrizability and Lindel¨of properties of subspaces of the Alexandroff duplicate. This characterization clarifies the potential for finding Michael spaces among the subspaces of Alexandroff duplicates.

Keywords

• Resolution
• Alexandroff duplicate
• Lindelöf property
• Michaeltype line