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...Exercises for the lecture ma algebraic topology solutions of mock exam spring semester exercise metric spaces let x d be a space give denition t b and r show that subset br is open with respect to c y pd all this denes new on i e also from part prove solution dened in u called if every there an such as set are observe hence then we have thus altogether proven any point solve has properties since xmapsr itself p moreover symmetric see triangle inequality holds note z square root function monotonically increasing obtain indeed concerning question bd balls radius around or respectively therefore likewise non negative half line implies form which shows it same argument proves connectedness continuous maps equipped their standard topologies s subspace denitions path connected discrete f map equal either constant value suppose hint no consider g topological tx two points exists disconnected empty subsets v not j induced by these sets theorem notes image must but saying assume property means ...