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Proposition: Inheritance of the $T_1$ Property

The $T_1$ separation property of topological spaces can be inherited as follows:

1. The $T_1$ property is hereditary, i.e. every topological subspace of a $T_1$ space is a $T_1$ space.
2. Every topological sum of $T_1$ spaces is a $T_1$ space.
3. Every topological sum of $T_1$ spaces is a $T_1$ space.

Table of Contents

Proofs: 1

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References

Bibliography

1. Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition
3. Grotemeyer, K.P.: "Topologie", B.I.-Wissenschaftsverlag, 1969