## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

# A Classification of Baire-1 Functions

P. Kiriakouli
Transactions of the American Mathematical Society
Vol. 351, No. 11 (Nov., 1999), pp. 4599-4609
Stable URL: http://www.jstor.org/stable/117963
Page Count: 11

#### Select the topics that are inaccurate.

Cancel
Preview not available

## Abstract

In this paper we give some topological characterizations of bounded Baire-1 functions using some ranks. Kechris and Louveau classified the Baire-1 functions to the subclasses B1 ξ(K) for every $\xi <\omega _{1}$ (where K is a compact metric space). The first basic result of this paper is that for $\xi <\omega$, f∈ B1 ξ +1(K) iff there exists a sequence (fn) of differences of bounded semicontinuous functions on K with fn→ f pointwise and γ ((fn))≤ ω ξ (where γ '' denotes the convergence rank). This extends the work of Kechris and Louveau who obtained this result for ξ =1. We also show that the result fails for ξ ≥ ω . The second basic result of the paper involves the introduction of a new ordinal-rank on sequences (fn), called the δ -rank, which is smaller than the convergence rank γ . This result yields the following characterization of B1 ξ(K): f∈ B1 ξ(K) iff there exists a sequence (fn) of continuous functions with fn→ f pointwise and δ ((fn))≤ ω ξ -1 if $1\leq \xi <\omega$, resp. δ ((fn))≤ ω ξ if ξ ≥ ω .

• 4599
• 4600
• 4601
• 4602
• 4603
• 4604
• 4605
• 4606
• 4607
• 4608
• 4609