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A CORRECTIOn TO THE PAPER "On A THEOREM OF LERAY"

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Science China Mathematics 1962年第5期 723-728页

作者： wu wen-ts■n

The statement of Theorem 1 of the paper "On a Theorem of Leray" in Vol.X, no. 7, 1961, of this iournal should be corrected to take the following form: Theorem 1. Let H be a cohomology theory defined on pairs of normal spaces which possess the strong excision property. Let E be a bicompact Hausdorff space with a finite closed covering F such that each non-empty intersection of sets in F has the same cohomology groups in dimensions up to r as those of a point, then the cohomology group in dimension r of E will be isomnorphic to that of the nerve complex K of the covering F, etc.

关键词：飞飞几几 A CORRECTIOn TO THE PAPER On A THEOREM OF LERAY

On THE PLAnAR IMBEDDInG OF LInEAR GRAPHS(COnTInUED)

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系统科学与数学 1986年第1期 23-35页

作者： wu wen-JUn (wu wen-ts(?)n) (Institute of Systems Science,Academia Sinica)

*** REDUCTIOn OF FUnDAMEnTAL SYSTEM OF LInEAR EQUATIOnSThe fundamental system of linear equations(If)in preceding Sect 4 can actuallybe put in a much simpler *** this purpose let us denote by nT a certain neigh-borhood of T in G sufficiently small so that the T-immersions considered will be someimbeddings when restricted on nT and that all possible intersections of images of dis-joint external edges are not in *** shall call these T-immersions also nT-immer-sions.

关键词： COnTInUED On THE PLAnAR IMBEDDInG OF LInEAR GRAPHS

On SQUARES In GRASSMAnnIAn MAnIFOLDS*

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Science China Mathematics 1953年第2期 91-115页

作者： wu wen-tsün (Institute of Mathematics, Academia Sinic)

InTRODUCTIOn The present paper gives detailed proofs of the results announced in a note published in the Comptes rendus of 1950. The author wishes to express his gratitude to M. H. Cartan for the help and encouragemen... 详细信息

关键词： On SQUARES In GRASSMAnnIAn MAnIFOLDS

A MECHAnIZATIOn METHOD OF GEOMETRY AnD Its APPLICATIOnS Ⅳ.SOME THEOREMS In PLAnAR KInEMATICS

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Systems Science and Mathematical Sciences 1989年第2期2卷 97-109页

作者：吴文俊 Institute of Systems Science Academa SinicaBeijingChina

Let a moving plane MP over a fixed plane FP occupy four different *** of such positions is associated with a center of rotation called pole so that we have a *** an illustration of our general method of mechanical theorem proving and discovering,we discuss in the present paper in some derails certain theorems connected with such a configuration.

关键词： Mathematics mechanization Mechanical theorem proving Kinematics Linkages Mechanical design

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On the notion of Imbedding Classes

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Science in China,Ser.A 1964年第4期 681-682页

作者：吴文俊

§1. Let ζ={（?）, X, ω} be an S°-bundle or a 2-sheeted covering having a base-connected polytope X, projection ω, and a structural group T consisting of two elements: 1 and t, with t operating without fixed points in （?）. For any coefficient group G, let G（ζ） be the system of local groups in X determined by the homomorphism φ:π1（X, x0）→AutG such that for any α∈π1（X, x0）, φ（α）（g）=+g or -g accord-

关键词： On the notion of Imbedding Classes

SOME REMARKS On MECHAnICAL THEOREM-PROVInG In ELEMEnTARY GEOMETRY

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Acta Mathematica Scientia 1983年第4期3卷 357-360页

作者：吴文俊 Institute of Systems Science Academia Sinica

In a previous paper (cf. [3]) we have pointed out that almost all theorems in ordinary geometry(i.e, ordinary euclidean geometry) are only generically true, or true only under some non-degeneracy) conditions usually not explicitely described in the statement of the theorem. This fact is quite fatal to make the usual euclidean fashion

关键词： SOME REMARKS On MECHAnICAL THEOREM-PROVInG In ELEMEnTARY GEOMETRY

On THE ISOTOPY OF COMPLEXES In A EUCLIDEAn SPACE Ⅰ

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Science in China,Ser.A 1960年第1期 21-46页

作者：吴文俊

The author has shown that the notion of reduced products of a space may be quite useful for topological problems of a non-homotopic character, and has applied this notion to the study of imbedding, immersion and isotopy of a space in a euclidean space and also some other related questions (cf. e. g. [1], and the references given there). Recently the author has shown furthert that given any two linear imbeddings of a finite complex in a euclidean space, invariants

关键词： On THE ISOTOPY OF COMPLEXES In A EUCLIDEAn SPACE pair

nOTES On COMPLEX MAnIFOLDS AnD ALGEBRAIC VARIETIES Ⅰ. PLūCKER’S FORMULA

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Science in China,Ser.A 1962年第5期 575-590页

作者：吴文俊 Institute of Mathematics Academia Sinica

§1. Let C be a plane algebraic curve of degree m, then its genusis given by the following Plucker’s formula (cf. e.g. [6], p. 103): p=(m-1)(m-2)/2-d-s, (1.1) in which d is the number of 'double points', and s=Σ(k-1... 详细信息

关键词： PL CKER’S FORMULA nOTES On COMPLEX MAnIFOLDS AnD ALGEBRAIC VARIETIES over 一砰

On THE REALIZATIOn OF COMPLEXES In EUCLIDEAn SPACES Ⅱ

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Science in China,Ser.A 1958年第4期 365-387页

作者：吴文俊 Institute of Mathematics Academia Sinica

For the realization problem of complexes or more general spaces in Euclidean spaces we maycite the following results:1° In 1932 van Kampen proved the existence of n-dimensional complexes K not realizablein Euclidean space of dimension *** proof depends on certain invariants deduced from the reduced 2-fold symmetric productK* of *** author has pointed out that van Kampen’s invariant is merely the extreme oneof a system of invariants Φm∈Hm （K*,I（m））,（I（m）=I or I2,depending on m being even orodd）,namely Φ2n,and Φm=0 is a necessary condition for K to be realizable in *** provedalso in [2] the topological invariance of Φm,i.e.,the independence of Φm of the chosen sub-division K of the space of K,while van Kampen,in the extreme case m=2n considered by him,has not even proved its combinatorial invariance.2°In the case of differentiable manifold,Whitney（cf.e.g.,[3]） has introduced a systemof invariants which the present author has called the dual Whitney classes m,and proved that k=0,k≥m-n （1）are necessary conditions for an n-dimensional closed differentiable manifold to be realizable in Rm,3° For compact Hausdorff spaces X,Thorn has proved（[4] Th.Ⅲ.25） the followingtheorem:Let Qi be certain operations deduced from Steenrod squares,thenQi Hr （X,I2）=0,2i+r≥m （2）are necessary conditions for X to be realizable in *** operations Qi were previously intro-duced by the author by applying Smith’s theory of periodic transformations and will henceforthbe denoted by Smi（cf.[5] and [6]）.Besides,Flores got also the same results as van Kampen’s concerning the existence ofn-dimensional complexes K not realizable in ***,what he used to prove his resultsis got by imbedding the first K in R2m+1,and is actually not an invariant,but depends ingeneral on the way of realization of K in R2n+*** will be explained further in the *** the various theories listed above,not only the methods used are quite different from oneanother,but also the objects and the realization conc

关键词： On THE REALIZATIOn OF COMPLEXES In EUCLIDEAn SPACES