Let-X-T-be-any-topological-space-Verify-that-the-intersection-of-any-finite-number-of-members-of-T-is-a-member-of-T-Use-mathematical-induction-to-prove-your-result-

Question Number 15850 by tawa tawa last updated on 14/Jun/17

$$\mathrm{Let}\:\left(\mathrm{X},\:\mathrm{T}\right)\:\mathrm{be}\:\mathrm{any}\:\mathrm{topological}\:\mathrm{space}\:.\:\mathrm{Verify}\:\mathrm{that}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{finite}\:\mathrm{number}\:\mathrm{of}\:\mathrm{members}\:\mathrm{of}\:\mathrm{T}\:\mathrm{is}\:\mathrm{a}\:\mathrm{member}\:\mathrm{of}\:\mathrm{T}.\:\mathrm{Use}\:\mathrm{mathematical} \\ $$$$\mathrm{induction}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{your}\:\mathrm{result}. \\ $$

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