Cratylus
Junior Member
- Joined
- Aug 14, 2020
- Messages
- 82
This is not homework. I looked everywhere how to do it
Let {xn:n∈Z } be a sequence in A in R which is monotone increasing or monotone descreasing.
Let f { xn:n∈Z } by f(xn )=n for each n. Then f is continuous on { xn:n∈Z+ } and if this set is a closed subset of A f can be extended to a continuous function F:A->R
Hint: suppose our sequence is monotone increasing .The intervals (xn,xn+1) and (n,n+1)are very much alike.. Patch together some restrictions of homeomorphism to get an extension of f
Sourace:A first source in topology .Robert Conover pg 144
Let {xn:n∈Z } be a sequence in A in R which is monotone increasing or monotone descreasing.
Let f { xn:n∈Z } by f(xn )=n for each n. Then f is continuous on { xn:n∈Z+ } and if this set is a closed subset of A f can be extended to a continuous function F:A->R
Hint: suppose our sequence is monotone increasing .The intervals (xn,xn+1) and (n,n+1)are very much alike.. Patch together some restrictions of homeomorphism to get an extension of f
Sourace:A first source in topology .Robert Conover pg 144
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