Descriptive properties of density preserving autohomeomorphisms of the unit interval

Szymon Głąb; Filip Strobin

Open Mathematics (2010)

  • Volume: 8, Issue: 5, page 928-936
  • ISSN: 2391-5455

Abstract

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We prove that density preserving homeomorphisms form a Π11-complete subset in the Polish space ℍ of all increasing autohomeomorphisms of unit interval.

How to cite

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Szymon Głąb, and Filip Strobin. "Descriptive properties of density preserving autohomeomorphisms of the unit interval." Open Mathematics 8.5 (2010): 928-936. <http://eudml.org/doc/269621>.

@article{SzymonGłąb2010,
abstract = {We prove that density preserving homeomorphisms form a Π11-complete subset in the Polish space ℍ of all increasing autohomeomorphisms of unit interval.},
author = {Szymon Głąb, Filip Strobin},
journal = {Open Mathematics},
keywords = {Density preserving homeomorphism; Coanalytic set; Π11-complete set; density-preserving homeomorphism; coanalytic set; -complete set},
language = {eng},
number = {5},
pages = {928-936},
title = {Descriptive properties of density preserving autohomeomorphisms of the unit interval},
url = {http://eudml.org/doc/269621},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Szymon Głąb
AU - Filip Strobin
TI - Descriptive properties of density preserving autohomeomorphisms of the unit interval
JO - Open Mathematics
PY - 2010
VL - 8
IS - 5
SP - 928
EP - 936
AB - We prove that density preserving homeomorphisms form a Π11-complete subset in the Polish space ℍ of all increasing autohomeomorphisms of unit interval.
LA - eng
KW - Density preserving homeomorphism; Coanalytic set; Π11-complete set; density-preserving homeomorphism; coanalytic set; -complete set
UR - http://eudml.org/doc/269621
ER -

References

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  1. [1] Bruckner A.M., Density-preserving homeomorphisms and a theorem of Maximoff, Quart. J. Math. Oxford, 1970, 21(3), 337–347 http://dx.doi.org/10.1093/qmath/21.3.337 Zbl0196.07701
  2. [2] Ciesielski K., Larson L., Ostaszewski K., ℐ -Density Continuous Functions, Mem. Amer. Math. Soc., 1994, 107(515) Zbl0801.26001
  3. [3] Głab S., Descriptive properties of families of autohomeomorphisms of the unit interval, J. Math. Anal. Appl., 2008, 343(2), 835–841 http://dx.doi.org/10.1016/j.jmaa.2008.01.068 Zbl1151.03024
  4. [4] Kechris A.S., Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156, Springer, New York, 1995 Zbl0819.04002
  5. [5] Niewiarowski J., Density-preserving homeomorphisms, Fund. Math., 1980, 106(2), 77–87 Zbl0447.28015
  6. [6] Ostaszewski K., Continuity in the density topology II, Rend. Circ. Mat. Palermo, 1983, 32(3), 398–414 http://dx.doi.org/10.1007/BF02848542 Zbl0564.26001

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