Affine bijections of C(X,I)
Studia Mathematica (2006)
- Volume: 173, Issue: 3, page 295-309
- ISSN: 0039-3223
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topJanko Marovt. "Affine bijections of C(X,I)." Studia Mathematica 173.3 (2006): 295-309. <http://eudml.org/doc/285219>.
@article{JankoMarovt2006,
abstract = {Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.},
author = {Janko Marovt},
journal = {Studia Mathematica},
keywords = {affine bijections; set of effects},
language = {eng},
number = {3},
pages = {295-309},
title = {Affine bijections of C(X,I)},
url = {http://eudml.org/doc/285219},
volume = {173},
year = {2006},
}
TY - JOUR
AU - Janko Marovt
TI - Affine bijections of C(X,I)
JO - Studia Mathematica
PY - 2006
VL - 173
IS - 3
SP - 295
EP - 309
AB - Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.
LA - eng
KW - affine bijections; set of effects
UR - http://eudml.org/doc/285219
ER -
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