Suppose \(X\) is a second countable space . Then \(X\) is a first countable space , a separable space and a Lindelöf space . [1, Theorem 2.50]
Remarks
- The converse is not true. Also no relation between first countable, separable and Lindelöf exist. [1, Problem 2-18].
- On metric spaces second countable, separable and Lindelöf is equivalent.
References Link to heading
- J. Lee, Introduction to Topological Manifolds. New York, NY: Springer New York, 2011. doi:10.1007/978-1-4419-7940-7