[分析] 有關topological vector space

[smarter1004 (請拒絕看各新聞台)]

大家好
小弟唸到topological vector space發現其很難想像
需要一點指點
Let V be a topological vector space(not necessarily Hausdorff).
Let W be a subspace of V (with E in W being open if and only if E being
an intersection of W and some open set in V).
Question 1: Is W a topological vector space?
Question 2: If the answer to question 1 is negative, please give me
a counterexample. What if W being finite-dimensional?
謝謝大家

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→ kerwinhui   : which category is W a subspce of V? TS/VS/TVS?
→ smarter1004 : W是V的 vector subspace, 若照topological subspace
→ smarter1004 : 的方式定義W的topology, 問此topology是否會使W 成
→ smarter1004 : 為TVS
→ kerwinhui   : (1) Yes, just look at subspace topology (2) N/A