# Let (X,dx) be a metric space and x in X. Show that f: X->R given by f(a)=dX(a,x) is continuous.?

• Let (X,dx) be a metric space and x in X. Show that f: X->R given by f(a)=dX(a,x) is continuous.?

Let (X,d) be a metric space. 1) ... (a,x) < r} 5) A subset S ⊆ X is bounded if there is an a ∈ X and an r ... Let f : X → Rbe a continuous function ...
Positive: 42 %
Let A ‰ X: If d is a metric for the topology of X, ... to show that f is injective. Given x1; ... Let Xn be a metric space with metric dn. (a) Show that ...
Positive: 39 %

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Let (X,d) be a metric space. Show ... (x)−g(x)|dx is a metric on C[a,b] the space ... Let A and B be closed subsets of X with A ∪B = X. Show that f is ...
Positive: 42 %
Solutions Chapter 1 1. |z 1 +z 2|2 +|z 1 − z ... (x−iy)(dx+idy)= ... let m→∞to show that |f n(z) ...
Positive: 37 %
Let Xbe a metric space with ... Assign to each p2Xthe function f p: X! R where f p(x) = d(p;x) d(a;x) ... f n(x)dx= 0: Solution: We are not given uniform ...