ℵ-spaces and spaces with a σ-hereditarily closure-preserving k-network

SPACES WITH σ-WEAKLY HEREDITARILY CLOSURE-PRESERVING sn-NETWORKS

We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99

Mapping theorems on א-spaces

In this paper we improve some mapping theorems on א-spaces. For instance we show that an א-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an א-space is preserved by a closed and open map.

Hereditarily Homogeneous Generalized Topological Spaces

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

σ-Normality of Topological Spaces

Interpolating Hereditarily Indecomposable Banach Spaces

A Banach space X is said to be Hereditarily Indecomposable (H.I.) if for any pair of closed subspaces Y , Z of X with Y ∩ Z = {0}, Y + Z is not a closed subspace. (Throughout this section by the term “subspace” we mean a closed infinite-dimensional subspace of X .) The H.I. spaces form a new and, as we believe, fundamental class of Banach spaces. The celebrated example of a Banach space with no...