Vol. 44, No. 2, 1973

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A topological lemma and applications to real functions

Clifford Edward Weil

Vol. 44 (1973), No. 2, 757–765

In working with functions of Baire class one having the Darboux property, one of the most useful tools has been a theorem due to Baire that says a function of Baire class one has a point of continuity on every closed set relative to the closed set. The lemma mentioned in the title can be used in many instances more efficiently than Baire’s theorem as is shown in §4. It is concerned with sets rather than functions and hence more basic than Baire’s Theorem, and easier to prove requiring only one application of Baire’s category theorem.

Mathematical Subject Classification 2000
Primary: 26A21
Secondary: 26A15, 26A69
Received: 10 August 1971
Published: 1 February 1973
Clifford Edward Weil