Subspace Topology on A: Calculate T_A

[Shaggydog4242]

Homework Statement

1. Let A= {a,b,c}. Calculate the subspace topology on A induced by the topology

T= { empty set, X,{a},{c,d},{b,c,e},{a,c,d},{a,b,c,e},{b,c,d,e},{c}, {a,c}} on X={a,b,c,d,e}.

Homework Equations

Given a topological space (X, T) and a subset S of X, the subspace topology on S is defined by

Ts= {S$\bigcap$U s.t. U$\in$T}

The Attempt at a Solution

Would it just be Ta = { emptyset, {a}, {c}, {b,c}, {a,c}, {a,b,c}, {b,c} }?

 

[Dick]

Homework Statement

1. Let A= {a,b,c}. Calculate the subspace topology on A induced by the topology

T= { empty set, X,{a},{c,d},{b,c,e},{a,c,d},{a,b,c,e},{b,c,d,e},{c}, {a,c}} on X={a,b,c,d,e}.

Homework Equations

Given a topological space (X, T) and a subset S of X, the subspace topology on S is defined by

Ts= {S$\bigcap$U s.t. U$\in$T}

The Attempt at a Solution

Would it just be Ta = { emptyset, {a}, {c}, {b,c}, {a,c}, {a,b,c}, {b,c} }?

Seems ok to me.