Second-countability is hereditary

This article gives the statement, and possibly proof, of a topological space property satisfying a topological space metaproperty
View all topological space metaproperty satisfactions | View all topological space metaproperty dissatisfactions
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Statement

Property-theoretic statement

The property of topological spaces of being a second-countable space satisfies the metaproperty of topological spaces of being hereditary.

Verbal statement

Any subspace of a second-countable space is second-countable under the subspace topology.

References

• Topology (2nd edition) by James R. Munkres, ^{More info}, Page 191, Chapter 4, Section 30