et D be a bounded open subset of RP. Suppose that f : D R is uniformly ontinuous. Show that we can define f on the closure D of D so that f is ontinuous on D and in fact uniformly continuous there. You may assume at every cluster point of D is the limit of a sequence of elements of D.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let D be a bounded open subset of RP. Suppose that f : D R is uniformly
continuous. Show that we can define f on the closure D of D so that f is
continuous on D and in fact uniformly continuous there. You may assume
that every cluster point of D is the limit of a sequence of elements of D.
Transcribed Image Text:Let D be a bounded open subset of RP. Suppose that f : D R is uniformly continuous. Show that we can define f on the closure D of D so that f is continuous on D and in fact uniformly continuous there. You may assume that every cluster point of D is the limit of a sequence of elements of D.
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