What is the definition of sequential precompactness?

Question

I know that topological space $X$ is called precompact if any sequence in $X$ has a subsequence convergent in X.

In my book of calculus of variation I have encountered the word sequential compactness.

What is the definition of sequential precompactness?

Thanks

Answer 1

According to your definition of precompactness, sequential compactness is just another name for it. I have encountered the notion of precompactness with a different meaning. Maybe sequential precompactness is the property that every sequence has a Cauchy subsequence, which is sometimes called just precompactness.