The Borel structure of iterates of continuous functions
1989 ◽
Vol 32
(3)
◽
pp. 483-494
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Keyword(s):
Let C[0,1] be the Banach space of continuous functions defined on [0,1] and let C be the set of functions f∈C[0,1] mapping [0,1] into itself. If f∈C, fk will denote the kth iterate of f and we put Ck = {fk:f∈C;}. The set of increasing (≡ nondecreasing) and decreasing (≡ nonincreasing) functions in C will be denoted by ℐ and D, respectively. If a function f is defined on an interval I, we let C(f) denote the set of points at which f is locally constant, i.e.We let N denote the set of positive integers and NN denote the Baire space of sequences of positive integers.
1985 ◽
Vol 101
(3-4)
◽
pp. 253-271
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1971 ◽
Vol 23
(3)
◽
pp. 468-480
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2016 ◽
Vol 19
(04)
◽
pp. 1650024
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1985 ◽
Vol 97
(1)
◽
pp. 137-146
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Keyword(s):
1989 ◽
Vol 31
(2)
◽
pp. 131-135
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1968 ◽
Vol 32
◽
pp. 287-295
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1976 ◽
Vol 19
(2)
◽
pp. 155-157
◽
1999 ◽
Vol 92
(2)
◽
pp. 107-118
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1997 ◽
Vol 55
(1)
◽
pp. 147-160
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Keyword(s):