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\({\mathcal I}\)-Density Continuous Functions
Krzysztof Ciesielski, Lee Larson, and Krzysztof Ostaszewski
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Memoirs of the American Mathematical Society
1994; 133 pp; softcover
Volume: 107
ISBN-10: 0-8218-2579-8
ISBN-13: 978-0-8218-2579-2
List Price: US$38
Individual Members: US$22.80
Institutional Members: US$30.40
Order Code: MEMO/107/515
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The classical approach to showing the parallel between theorems concerning Lebesgue measure and theorems concerning Baire category on the real line is restricted to sets of measure zero and sets of first category. This is because classical Baire category theory does not have an analogue for the Lebesgue density theorem. By using \({\mathcal I}\)-density, this deficiency is removed, and much of the structure of measurable sets and functions can be shown to exist in the sense of category as well. This monograph explores category analogues to such things as the density topology, approximate continuity, and density continuity. In addition, some questions about topological semigroups of real functions are answered.

Readership

Research mathematicians.

Table of Contents

  • The ordinary density topology
  • Category analogues of the density topology
  • \(\mathcal I\)-density continuous functions
  • Semigroups
  • Appendix A. Notation
  • References
  • Index
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