• Title/Summary/Keyword: weak M-semicontinuity

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SOME GENERALIZATIONS OF WEAKLY M-SEMI-CONTINUOUS AND WEAKLY M-PRECONTINUOUS FUNCTIONS

  • Noiri, Takashi;Popa, Valeriu
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.2
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    • pp.229-253
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    • 2016
  • As a generalization of (i, j)-weakly m-continuous functions [43], we introduce the notion of weakly M(i, j)-continuous functions and obtain many characterizations and some properties of the functions. We show that the function is a unified form of some functions between m-spaces and certain kinds of weakly continuous functions in bitopological spaces.

A NEW PROOF OF MACK'S CHARACTERIZATION OF PCS-ALGEBRAS

  • Kim, Hyoung-Soon;Woo, Seong-Choul
    • Communications of the Korean Mathematical Society
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    • v.18 no.1
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    • pp.59-63
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    • 2003
  • Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.