• 대한수학회보
• /
• 제41권4호
• /
• pp.665-676
• /
• 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.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.905-913
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제2권2호
• /
• pp.149-156
• /
• 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)

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제3권2호
• /
• pp.117-122
• /
• 1996

We investigate that if M is a compact subset of c-first countable space X, then ${\chi}{\in} A_u(M)$ if and only if $J(\chi){\neq}{\phi}{\subset}M$.

• 충청수학회지
• /
• 제7권1호
• /
• pp.109-115
• /
• 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.

• East Asian mathematical journal
• /
• 제32권3호
• /
• pp.365-375
• /
• 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.