Infinite-dimensionality modulo absolute Borel classes

• Autorzy: Chatyrko V. , Hattori Y.
• Języki publikacji: EN

Abstrakty

EN

For each ordinal 1 ≤ α < ω ₁ we present separable metrizable spaces Xα, Yα and Zα such that (i) f Xα, f Yα, f Zα = ωo, where f is either trdef or Ko-trsur, (ii) A(α)-trind Xα = ∞ and M(α)-trind Xα = -1, (iii) A(α)-trind Yα = -1 and M(α)-trind Zα = ∞, and (iv) A(α)-trind Zα = M(α)-trind Zα = ∞ and A(α + 1) ∩ M(α + l)-trind Zα = -1. We also show that there exists no separable metrizable space Wa with A(α)-trind Wα ≠ ∞, M(α)-trind Wα ≠ ∞ and A(α) ∩ M(α)-trind Wα = ∞, where A(α) (resp. M(α)) is the absolutely additive (resp. multiplicative) Borel class.

Słowa kluczowe

EN

small transfinite inductive dimension modulo P; separable metrizable space; absolute Borel class

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 2
• Strony: 163--176
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Chatyrko V.

autor

Hattori Y.

• Department of Mathematics, Linköping University, 581 83 Linköping, Sweden,

Bibliografia

• [1] J. M. Aarts and T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993.
• [2] M. G. Charalambous, On transfinite inductive dimension and deficiency modulo a class P, Topology Appl. 81 (1997) 123-135.
• [3] R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann, Lemgo, 1995.
• [4] A. Lelek, Dimension and mappings of spaces with finite deficiency, Colloq. Math. 12 (1964), 221-227.
• [5] E. Pol, The Baire-category method in some compact extension problems, Pacific J. Math. 122 (1986), 197-210.
• [6] -, On transfinite inductive compactness degree, Colloq. Math. 53 (1987), 57-61.
• [7] L. R. Rubin, R. M. Schori and J. J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), 93-102.
• [8] S. M. Srivastava, A Course on Borel Sets, Springer, New York, 1998.