• Title/Summary/Keyword: C-first countable space

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ASYMPTOTIC STABILITY IN GENERAL DYNAMICAL SYSTEMS

  • Lim, Young-Il;Lee, Kyung-Bok;Park, Jong-Soh
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.665-676
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    • 2004
  • In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

METRIZABILITY AND SUBMETRIZABILITY FOR POINT-OPEN, OPEN-POINT AND BI-POINT-OPEN TOPOLOGIES ON C(X, Y)

  • Barkha, Barkha;Prasannan, Azhuthil Raghavan
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.905-913
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    • 2022
  • We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

LIMIT SETS AND PROLONGATIONAL LIMIT SETS IN DYNAMICAL POLYSYSTEMS

  • Gu, Yoon-Hoe;Ry, Dae-Hee
    • The Pure and Applied Mathematics
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    • v.2 no.2
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    • pp.149-156
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    • 1995
  • In stability theory of polysystems two concepts that playa very important role are the limit set and the prolongational limit set. For the above two concepts, A.Bacciotti and N.Kalouptsidis studied their properties in a locally compact metric space [2]. In this paper we investigate their results in c-first countable space which is more a general space than a metric space.(omitted)

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Stability of Dynamical Polysystems

  • Gu, Yoon Hoe
    • Journal of the Chungcheong Mathematical Society
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    • v.7 no.1
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    • pp.109-115
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    • 1994
  • We introduce the concept of the prolongation operator and examine some properties of this operator. In c-first countable space X, we prove that each compact subset M of X is stable if and only if DR(M)=M for each polydynamical system.

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A NOTE ON SPACES DETERMINED BY CLOSURE-LIKE OPERATORS

  • Hong, Woo Chorl;Kwon, Seonhee
    • East Asian mathematical journal
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    • v.32 no.3
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    • pp.365-375
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    • 2016
  • In this paper, we study some classes of spaces determined by closure-like operators $[{\cdot}]_s$, $[{\cdot}]_c$ and $[{\cdot}]_k$ etc. which are wider than the class of $Fr{\acute{e}}chet-Urysohn$ spaces or the class of sequential spaces and related spaces. We first introduce a WADS space which is a generalization of a sequential space. We show that X is a WADS and k-space iff X is sequential and every WADS space is C-closed and obtained that every WADS and countably compact space is sequential as a corollary. We also show that every WAP and countably compact space is countably sequential and obtain that every WACP and countably compact space is sequential as a corollary. And we show that every WAP and weakly k-space is countably sequential and obtain that X is a WACP and weakly k-space iff X is sequential as a corollary.