Determine which of the following collection of subsets of R are bases: solve each one individually.

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Determine which of the following collection of subsets of R are bases: solve each one individually.

a) C1 = {(n,n+2) ⊆ R | n∈Z}

b) C2 = {[a,b] ⊆ R | a<b}

c) C3 = {[a,b] ⊆ R | a<=b}

d) C4 = {(-x,x) ⊆ R | x∈R}

e) C5 = {(a,b) ∪ {b+1} ⊆ R | a<b}

Let B be the collection of subsets of Z used in defining the digital line topology. Show that B is a basis for a topology Z.

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