位相空間上에서의 緊密性에 對한 硏究

李德世 충주대학교 1978 한국교통대학교 논문집 Vol.11 No.1

The concept of compactness is motivated by the property of a closed and bounded interval as stated in the classical Heine-Borel Theorem. Namely, a subset A of atoplogical spacex is compact if every open cover of A is reducible to finite cover. In this thesis, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. That is, by this time, there are several explanations of the property on the compactness as the dishevelled hair, but essentially, there is nothing combinated these so I am going to explain chiefly that these can combine as one in this thesis. This theor is the proof simplifing three expressins that I explain on atopological space by-A-for I define. A topological space (X,T) has-A-from iff the empty set is the only subset which is both closed and compact set. 1) For every point ????, {??} has a closed proper subset which is non-empty. 2) {??} is an infinite set to every point X, and if a topological space X is To, 3) For every point?? inX, {??} is an infinite set then the space X is an A-space.

緊密空間의 特性에 關한 硏究

李德世 충주대학교 1983 한국교통대학교 논문집 Vol.16 No.1

The concept of campactness is motivated by the property of a closed and bounded interval as stated in the classical Heine-Borel theorem. Namely, a subset A of a topological space X is compact if every open cover of A is reducible to finite cover. In this thesis, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. That is, A topological space (X, T) has A-form if the empty set in the only subset which is both closed and compact set. {χ} is an infinite set to every point χ, and if a topological space X is To and for every point χ in X {χ} is an infinite set then the space X is an A-space.

Lagrange 補間多項式에 關한 硏究

李德世 忠州大學校 1984 한국교통대학교 논문집 Vol.17 No.1

In this thesis, I am going to reconsider a Lagrange intepolation formula for unequally spaced data, one of the characteristics in a interpolation space, and study the characteristic laying on it. That is, suppose that we are given n+1 data points, ?? and we wish to find the coefficient Co, C₁‥‥‥‥‥C?? of the polynomial ?? (1. 1) such that the curve represented by Eq. (1.1) will pass through all n + 1 distinct points, That is, ?? (1. 2) We now define the Lagrange polynomial L??(χ) of degreen as ?? = 0 i f i ≠ k (1. 3) = 1 i f i = k (1. 4) where ?? are the given n + 1 distinct arguments. We can now write P??(χ) in the form ?? as is readily seen since we can obtain Eq. (1. 2) when each χ??-value(??=0, 1, …, n) is substitutea into Eq (1. 5) and when Eq. (1. 3) are taken into consideration.

긴밀공간의 동치관계에 관한 연구

李德世 忠州大學校 1996 한국교통대학교 논문집 Vol.31 No.2

The concept of compactness is motivated by the property of a closed and bounded interval as stated in the classical Heine-Borel theorem. In this paper, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. this theorem is the proof simplyfing three expressions that I explain on the topological space by A-form I define.

Hausdorff 空間의 性質에 對한 硏究

李德世 충주대학교 1977 한국교통대학교 논문집 Vol.10 No.1

(A study on property of Hausdorff space) A topological space×is a Hausdorffspace iff it satisfies the following axiom: Each pair of distinct points a, be×belong respectivily to disjoint open sets. In other words, there exist open sets Gand H such that. a∈G, b∈H and G∩H=ø. Hausdorff made a great contribution to analytical theory, which was the theory leading the method about neighberhood system in a study by a theory of topological space. Hence, I considered and studied the definition by Hausdorff space and the relation about itsproperty.

緊密 空間上의 特殊性質에 關하여

李德世 충주대 2000 한국교통대학교 논문집 Vol.35 No.2

A subset A of a topological space X is compact set if every open cover of A is redusible to finite cover. In this theses, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. A toplogical space(X, T) has A-form ifs the empty set is the only subset which is both closed and compact set. The following condition is equivalent: 1) (X, T) has a closed and compact subset which is the only empty set. 2) For every open set U≠X, there exists an open set U* which is U⊂U*≠X. 3) For every open set U≠X, there is X=U{Uα|Uα∈Φ} Which is a chain Φ ={Fα}of a open set which is U□Uα≠X.

位相空間上에서의 Homeomorphism空間에 對한 硏究

李德世 忠州大學校 1980 한국교통대학교 논문집 Vol.13 No.2

Two topological spaces X and Y are called homeomorphic or topologically equivalent if there exits abijective (????One-One, Onto) function f:x→v such that ??and?? are continuous. The function ?? called a homeomorphism. That is, by this time, there are several explanations of the property on the homeomorphism as the dishevelled hair. So I am going to proof The following Theorem. Let f be a 1:1 mapping from a set X onto a set Y. Let topological structure be defined on X and Y by the closure operators c and d, respectively. Then ??is a homeomorphism from (X,??(c)) to Y,??(d))??? for all sets A⊂X, ??(A??)= (??(A))??

位相空間의 緊密性에 關한 硏究

李德世 충주대 2001 한국교통대학교 논문집 Vol.36 No.2

The concept of compactness is motivated by the property of a closed and bounded interval as stated in the classical Heine-Borel theorem. In this theses, 1 am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. A topological space(X, T) has A-form if the empty set is the only subset which is both closed and compact set. The following condition is equivalent : 1) (X, T) has a closed and compact subset which is the only empty set. 2) For every open set U≠X, there is X=U{Uα | Uα∈Ø} which is a chain Ø={Fα} of a open set which is U□U≠X.

緊密 空間의 性質에 관한 硏究

李德世 忠州大學校 1973 한국교통대학교 논문집 Vol.6 No.-

A subset A of a topological space X is compact if every open cover of A is reducible to finite cover. In this thesis, I am going to reconsider a compactness, one of the property in a topological space, and lead the property laid on it. That is, by this time, there are several explanations of the property on the compactness as the dishevelled hair, but essentially, there is nothing combined these. So I am going to explain chiefly that these can combine as one in this thesis. This theorem is the proof simplifing six expressions that I explain to the keep point of a topological space. The following condition is equivalent: (1) (X,T) has a closed subset and a compact which is the only empty set. (2) a non-empty closed subset on (X,T) has a non-empty closed proper subset. (3) For every open set U ≠X, there exist an open set U* which is U??U*≠X. (4) For every open set U≠X, there is X=U{U????????} which is a chain ??={??} of a open set which is U??U???X. (5) For every non-empty closed set F, there exist a chain ??={??} of a non-empty closed subset of F, such that is ??{F????F????????}=??. (6) For every point x??X, ???? has a closed proper subset which is non-empty.

緊密集合이 閉鎖되어 있지 않은 工間에 對하여

李德世 忠州大學校 1974 한국교통대학교 논문집 Vol.7 No.-

"A study on spaces in which compact sets are never closed." The compact sets are to be a property that gives topological spaces that satisfy it with a structure similar to that possessed by closed and bounded sets in Euclidean spaces. In this thesis, I am going to reconsider a compactness, one of the characteristics in a topological space, and study the characteristic laying on it. That is, let P be the set of positive integers and let consist of ø, P and On={1,2,‥‥‥ ,n} for n=1,2, ‥‥‥ Then (P.τ) has following property: the empty set is the only subset of P which is both closed and compact. In this note we will give several characterizations of this property and list some of its implications.