摘要:

We consider bases in matroids of infinite rank, and prove: (a) the existence of a perfect matching in the ‘transition graph’ of any two bases. This is an extension of the existence of a non‐zero generalized diagonal in the transition matrix between bases in finite dimensional linear spaces, and settles a conjecture of the second author [8]. (b) A Cantor‐Bernstein theorem for matroids. (c) The existence of a winning strategy for the ‘good guy’ in an exchange game between bases in infinite matroids.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.385

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Chetwynd and Hilton showed that any regular simple graph with even ordernand maximum degree at least ⅚nhas chromatic index equal to its maximum degree. We show how to extend this result to general multigraphs, including those of odd order. This also verifies a special case of conjectures by Goldberg and Seymour.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.393

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.401

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.420

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.437

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In the present paper, we introduce a Riemann definite integral with values in an arbitrary metric space and describe its basic properties. This integral is a generalization of the classical Riemann—Stieltjes definite integral as well as a generalization of solutions of the differential equations of the typey′ =f(x,y).

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.445

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.463

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.476

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We give a modified form of the mountain pass lemma which does not require the Palais‐Smale condition. Some applications are presented.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.491

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

IfZis a quotient of a subspace of a separable Banach spaceX, andVis any separable Banach space, then there is a Banach couple (A0,A1) such thatA0andA1are isometric toX⊕V, and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic toZ. Thus many properties of Banach spaces, including having non‐trivial cotype, having the Radon–Nikodym property, and having the analytic unconditional martingale difference sequence property, do not pass to intermediate spaces.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-44.3.503

出版商:Oxford University Press    

年代:2016

数据来源: WILEY