Sequentially closed subset

This article defines a property over pairs of a topological space and a subspace, or equivalently, properties over subspace embeddings (viz, subsets) in topological spaces

Definition

A subset of a topological space is termed sequentially closed if given any convergent sequence of points in the subset(viz, a sequence of points that has a limit in the whole space), every limit of the sequence lies inside the subset.

Relation with other properties

Stronger properties

• Closed subset: The two properties become equivalent in sequential spaces