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2 results

  • The proximally continuous integrals

  • Part of
  • D. N. Sarkhel, A. K. De
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 31 / Issue 1 / June 1981
    Published online by Cambridge University Press:
    09 April 2009, pp. 26-45
    Print publication:
    June 1981
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  • This paper introduces certain generalization of the notions of approximate limit, continuity and derivative and of absolute continuity, of real functions, leading to generalized integrals of Perron and Denjoy types comprising the AP-integral of Burkill (1931) and Sonouchi and Utagawa (1949) and the AD-integral of Kubota (1963), respectiely. The generalizations are all substantiated by appropriate examples.

  • Hausdorff Compactifications as Epireflections

  • W. N. Hunsaker, S. A. Naimpally
  • Journal:
    Canadian Mathematical Bulletin / Volume 17 / Issue 5 / February 1975
    Published online by Cambridge University Press:
    20 November 2018, pp. 675-677
    Print publication:
    February 1975
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  • We answer the following problem posed by Herrlich in the affirmative: “Can the Freudenthal compactification be regarded as a reflection in a sensible way?” This is accomplished by exploiting the one-to-one correspondence between proximities compatible with a given Tihonov space and compactifications of that space. We give topological characterizations of proximally continuous functions for the proximities associated with the Freudenthal and Fan-Gottesman compactifications.