• 호남수학학술지
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• 제31권2호
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• pp.233-237
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• 2009

In this paper, we show that: (1) every strongly ${\omega}$-monolithic space X with countable fan-tightness is Fr$\'{e}$chet-Urysohn; (2) a direct proof of that X is Lindel$\"{o}$f when $C_p$(X) is Fr$\'{e}$chet-Urysohn; and (3) X is Lindel$\"{o}$f when X is paraLindel$\"{o}$f and $C_p$(X) is AP. (3) is a generalization of the result of [8]. And we give two questions related to Fr$\'{e}$chet-Urysohn and AP properties on $C_p$(X).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권2호
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• pp.191-201
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• 2023

In this paper the control system described by Urysohn type integral equation is studied. It is assumed that control functions are integrally constrained. The trajectory of the system is defined as multivariable continuous function which satisfies the system's equation everywhere. It is shown that the set of trajectories is Lipschitz continuous with respect to the parameter which characterizes the bound of the control resource. An upper estimation for the diameter of the set of trajectories is obtained. The robustness of the trajectories with respect to the fast consumption of the remaining control resource is discussed. It is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the control resource.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.491-503
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• 2001

In this paper we show that solution set of certain Volterra inclusions on the half line is a continuum.

• 대한수학회논문집
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• 제22권2호
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• pp.297-303
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• 2007

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

• 대한수학회논문집
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• 제23권3호
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• pp.447-452
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• 2008

We provide some examples around AP and WAP spaces which are connected with higher convergence properties-radiality, semiradiality and pseudoradiality. We also prove a theorem (Theorem 3.2) that (a) any pseudo-open continuous image of an AP-space is an AP-space and (b) any pseudo-open continuous image of an WAP-space is an WAP-space. This answers the question posed by V. V. Tkachuk and I. V. Yaschenko [10].

• 호남수학학술지
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• 제39권4호
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• pp.655-663
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• 2017

In this paper we define $AP_c$ and $AP_{cc}$ spaces which are stronger than the property of approximation by points(AP). We investigate operations on their subspaces and study function theorems on $AP_c$ and $AP_{cc}$ spaces. Using those results, we prove that every continuous image of a countably compact Hausdorff space with AP is AP. Finally, we prove a theorem that every compact ${\kappa}$-WAP space is ${\kappa}$-pseudoradial, and prove a theorem that the product of a compact ${\kappa}$-radial space and a compact ${\kappa}$-WAP space is a ${\kappa}$-WAP space.

• 대한수학회논문집
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• 제9권2호
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• pp.423-438
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• 1994

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) ＋ $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f ＋ Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$ ⊂ $L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)