• Title/Summary/Keyword: lower and upper semicontinuous

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CATEGORICAL PROPERTIES OF SEMI-CONTINUOUS QUASI-ORDERED SPACES

  • Shin, Seon-Ho
    • Communications of the Korean Mathematical Society
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    • v.17 no.4
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    • pp.681-691
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    • 2002
  • We study categorical properties of the category SWQOS (S$\^$U/WQOS, S$\^$L/WQOS, resp) of (upper, lower, resp.) semi-continuous quasi-ordered spaces and the subcategory SWPOS (S$\^$U/WPOS, S$\^$L/WPOS, resp.) of (upper, lower, resp.) semicontinuous partially ordered spaces. We show that the categories S$\^$U/WPOS, S$\^$L/WPOS and SWPOS are closed under the formation of initial mono-sources in the category TQOS of topological quasi-ordered spaces, and they we mono-topological, complete and cocomplete epireflective subcategories of the category TQOS. We obtain their MacNeille and universal initial completions, as well as those of subcatego.ies S$\^$U/WQOS(S$\^$L/WQOS) and SWQOS, in which the topologies are T$\_$0/ and T$_1$, respectively.

CONTINUITY OF THE ORBITAL AND LIMIT SET MAPS IN GENERAL DYNAMICAL SYSTEMS

  • Lee, Kyung-Bok;Park, Jong-Suh
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.649-660
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    • 2011
  • S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps, K(x) and L(x), where K and L are considered as maps from X to $2^X$. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.