# Descriptive properties of density preserving autohomeomorphisms of the unit interval

Open Mathematics (2010)

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

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topSzymon 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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- [2] Ciesielski K., Larson L., Ostaszewski K., $\mathcal{I}$ -Density Continuous Functions, Mem. Amer. Math. Soc., 1994, 107(515) Zbl0801.26001
- [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] Kechris A.S., Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156, Springer, New York, 1995 Zbl0819.04002
- [5] Niewiarowski J., Density-preserving homeomorphisms, Fund. Math., 1980, 106(2), 77–87 Zbl0447.28015
- [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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