Compactness implies countably compactness which in turn implies limit-point compactness. 

Sequentially compactness implies limit point compactness. 

$Z\_{+} \times \{0,1\}$ with two-point indiscrete space $\{0,1\}$ is limit-point compact but not sequentially compact. 

First uncountable ordinal is sequentially compact, countably compact, but not compact. 

Can anybody give me any examples for 

1. Sequentially compact but not countably compact space (hence limit-point compact but not compact)
2. Countably compact but neither compact nor sequentially compact space.

?

Thanks in advance.