Mathematics, 15.10.2019 18:30 ryndersava
3. recall that p is a condensation point of s if each mrp contains uncountably many points of s. the set of condensation points of s is denoted as sβ. prove: (a) if s β t then sβ β tβ. (b) (s βͺ t)β = sβ βͺ tβ. (c) sβ β sβ where sβ = (s)β (d) sβ is closed in m; that is, sβ β sβ where sβ = (sβ) . (e) sββ β sβ where sββ = (sβ)β. (f) calculate nβ, qβ, rβ, and (r q)β. (g) give an example showing that sβ can be a proper subset of (s)β. thus, (c) is not in general an equality
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3. recall that p is a condensation point of s if each mrp contains uncountably many points of s. the...
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