• East Asian mathematical journal
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• 제17권2호
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• pp.185-189
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• 2001

In this paper we study on $Fr\'{e}chet$-Urysohn expansions of topological spaces, countable $Fr\'{e}chet$-Urysohn spaces and Hausdorff $Fr\'{e}chet$-Urysohn spaces.

• 호남수학학술지
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• 제37권4호
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• pp.549-557
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• 2015

We introduce strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces which are stronger than ${\kappa}$-$Fr{\acute{e}}chet$ and ${\kappa}$-net spaces respectively. For convenience, we use the terminology "${\kappa}$-sequential" instead of "${\kappa}$-net space", introduced by R.E. Hodel in [5]. And we study some properties and topological operations on such spaces. We also define strictly ${\kappa}$-$Fr{\acute{e}}chet$ and strictly ${\kappa}$-sequential spaces which are more stronger than strongly ${\kappa}$-$Fr{\acute{e}}chet$ and strongly ${\kappa}$-sequential spaces respectively.

• 호남수학학술지
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• 제20권1호
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• pp.79-88
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• 1998

In this paper we define the concept of $Fr{\acute{e}}chet$ function algebras on hemicompact spaces. So we show that under certain condition they can be represented as a projective limit of Banach function algebras. Then the class of $Fr{\acute{e}}chet$ Lipschitz algebras on hemicompact metric spaces are defined and their relations with the class of lipschitz algebras on compact metric spaces are studied.

• 대한수학회지
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• 제44권2호
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• pp.261-273
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• 2007

In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\'{e}chet$-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\'{e}chet-Urysohn$, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\'{e}chet-Urysohn$. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\'{e}chet-Urysohn$. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.

• East Asian mathematical journal
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• 제14권1호
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• pp.141-148
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• 1998

• East Asian mathematical journal
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• 제24권1호
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• pp.97-103
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• 2008

New fixed point theorems for permissible maps between $Fr{\acute{e}}chet$ spaces are presented. The proof relies on index theory developed by Dzedzej and on viewing a $Fr{\acute{e}}chet$ space as the projective limit of a sequence of Banach spaces.

• East Asian mathematical journal
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• 제32권3호
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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.

• 호남수학학술지
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• 제34권1호
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• pp.85-92
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• 2012

Our purpose of this paper is to introduce and study some properties related to approximations by points. More precisely, we introduce strongly AP, strongly AFP, strongly ACP, and strongly WAP properties which are stronger than AP, AFP, ACP, and WAP respectively. Also they are weaker than strongly Fr$\acute{e}$chet property. And we study general properties and topological operations on such spaces and give some examples.

• 충청수학회지
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• 제28권4호
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• pp.513-523
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• 2015

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

• 대한수학회논문집
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• 제13권2호
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• pp.359-365
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• 1998

We give two sufficient conditions that the space (X,C*) be a Fr$\acute{e}$chet-Urysohn space such that $x_n \to x$ in (X,c) if and only if $x_n \to x$ in (X,c*), where c* is the sequential closure operator on a generalized topological (X,c).