Descriptive properties of density preserving autohomeomorphisms of the unit interval

• Autorzy: Szymon Głąb , Filip Strobin
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Density preserving homeomorphism; Coanalytic set; Π11-complete set

Kategorie tematyczne

• 03E15: Descriptive set theory
• 26A30: Singular functions, Cantor functions, functions with other special properties
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 5
• Strony: 928-936

Daty

wydano

2010-10-01

online

2010-09-28

Twórcy

autor

Szymon Głąb

• Technical University of Łódz

autor

Filip Strobin

Bibliografia

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

Identyfikatory

DOI

10.2478/s11533-010-0054-z