An example of a hereditarily normal topologically finite space, which is topologically infinite relative to the class of all its proper F σ-subspaces

Abstract

Abstract A (Hausdorf) hereditarily normal (not perfectly normal) space X is constructed, which has the following properties: (a) there exists a proper open subspace of X which is homeomorphic to the whole X (i.e., the space X is topologically infinite); (b) the space is homeomorphic to none of its proper {F_{\sigma}} -subspaces (i.e., the space X is topologically finite relative to the class of all its proper {F_{\sigma}} -subspaces).