ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.417

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Dendrons and their products admit a natural, continuous median operator. We prove that there exists a two‐dimensional metric continuum with a continuous median operator, for which there is no median‐preserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negatively, and is sharply contrasting with a result of Stralka [15]on embeddings of compact lattices.

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.439

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Results are obtained concerning normal subgroups of the automorphism groups of certain infinite trees. These structures are mostly ℵo‐categorical, and are trees in a poset‐theoretic but not graph‐theoretic sense. It is shown that the automorphism group has a smallest non‐trivial normal subgroup, a largest proper normal subgroup, and at least 22οnormal subgroups between these two. We also obtain and use some results on groups of automorphisms of chains.

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.454

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper and its predecessor examine certain infinite semilinear orders (‘trees’) and their automorphism groups. Here we classify weakly 2‐transitive trees up toL∞ο‐equivalence, and countable weakly 2‐transitive trees up to isomorphism. Various results are obtained about the automorphism groups, concerning torsion, divisibility, and subgroups of small index. The automorphism groups of some related treelike structures and their normal subgroup lattices are also examined.

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.479

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.495

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.519

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.550

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.559

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Operators without non‐trivial invariant subspaces (so called ‘cyclic operators’) are now known to exist on a number of Banach spaces, but all such Banach spaces are non‐reflexive and contain copies of the sequence spacel1In this paper, we find cyclic operators on some new Banach spaces which do not containl1. The Banach spaces involved are not reflexive, but they include the space co, which has separable dual, and a spacej∞(thel2direct sum of countably many copies of the James space J) which has a separable bidual (indeed, all the spacesJ∞*,J∞**,J∞***and so on, are separable). This seems to be a best possible result, short of finding a solution to the invariant subspace problem on a reflexive Banach space.

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.583

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-58.3.608

出版商:Oxford University Press    

年代:2016

数据来源: WILEY