A factorization theorem for the transfinite kernel dimension of metrizable spaces
نویسنده
چکیده
We prove a factorization theorem for transfinite kernel dimension in the class of metrizable spaces. Our result in conjunction with Pasynkov’s technique implies the existence of a universal element in the class of metrizable spaces of given weight and transfinite kernel dimension, a result known from the work of Luxemburg and Olszewski.
منابع مشابه
Universal spaces in the theory of transfinite dimension, II
We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension ω0, or, equivalently, of small transfinite dimension ω0; that is, the family consists of compact metrizable spaces whose transfinite dimension is ω0, and every compact metrizable space with transfinite dimension ω0 is embeddable in a space of the ...
متن کاملDecomposing Borel Functions Using the Shore-slaman Join Theorem
Jayne and Rogers proved that every function from an analytic space into a separable metrizable space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each Fσ set under it is again Fσ . Many researchers conjectured that the JayneRogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-S...
متن کاملThe Transfinite Hausdorff Dimension
Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...
متن کامل1 1 M ay 2 00 4 EXTENSION DIMENSION AND QUASI - FINITE CW - COMPLEXES
We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications. Several results related to the class of quasi-finite complexes are established, such as completion of metrizable spaces, existence of universal spaces and a ve...
متن کاملExtensional Dimension and Completion of Maps
We prove the following completion theorem for closed maps between metrizable spaces: Let f : X → Y be a closed surjection between metrizable spaces with e-dimf ≤ K, e-dimX ≤ LX and e-dimY ≤ LY for some countable CW -complexes K, LX and LY . Then there exist completions X̃ and Ỹ of X and Y , respectively, and a closed surjection f̃ : X̃ → Ỹ extending f such that e-dimf̃ ≤ K, e-dimX̃ ≤ LX and e-dimỸ ≤...
متن کامل