• Title/Summary/Keyword: d-complete topological space

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FIXED POINT THEOREMS IN d-COMPLETE TOPOLOGICAL SPACES

  • Cho, Seong-Hoon;Lee, Jae-Hyun
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.1009-1015
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    • 2010
  • We prove the existence of common fixed points for three self mappings satisfying contractive conditions in d-complete topological spaces. Our results are generalizations of result of Troy L. Hicks and B. E. Roades[Troy L. Hicks and B. E. Roades, Fixed points for pairs of mappings in d-complete topological spaces, Int. J. Math. and Math. Sci., 16(2)(1993), 259-266].

METRIZATION OF THE FUNCTION SPACE M

  • Lee, Joung-Nam;Yang, Young-Kyun
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.391-399
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    • 2003
  • Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

ON SUPER CONTINUOUS FUNCTIONS

  • Baker, C.W.
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.17-22
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    • 1985
  • B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

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