Connected and Sequentially Compact Rectifiable Spaces

Abstract

In this note, we mainly investigate the connected, sequentially compact and κ-Frechet-Urysohn properties of rectifiable spaces. It is showed that: (1) If G is a locally σ-sequentially compact rectifiable space with the Souslin property, then G is σ-sequentially compact; (2) Every connected locally σ-compact rectifiable space G is σ-compact; (3) If every compact (resp. countably compact, sequentially compact) subspace of a rectifiable space G is Frechet-Urysohn, then every compact (resp. countably compact, sequentially compact) sub- space of G is strongly Frechet-Urysohn. These results generalize the corresponding results in topological groups.