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Natural operators between vector valued differential forms

Cap, Andreas (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]This paper is devoted to a method permitting to determine explicitly all multilinear natural operators between vector-valued differential forms and between sections of several other natural vector bundles.

Nearly disjoint sequences in convergence l -groups

Ján Jakubík (2000)

Mathematica Bohemica

For an abelian lattice ordered group G let G be the system of all compatible convergences on G ; this system is a meet semilattice but in general it fails to be a lattice. Let α n d be the convergence on G which is generated by the set of all nearly disjoint sequences in G , and let α be any element of G . In the present paper we prove that the join α n d α does exist in G .

Neighborhood base at the identity of free paratopological groups

Ali Sayed Elfard (2013)

Topological Algebra and its Applications

In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.

Network character and tightness of the compact-open topology

Richard N. Ball, Anthony W. Hager (2006)

Commentationes Mathematicae Universitatis Carolinae

For Tychonoff X and α an infinite cardinal, let α def X : = the minimum number of α  cozero-sets of the Čech-Stone compactification which intersect to X (generalizing -defect), and let rt X : = min α max ( α , α def X ) . Give C ( X ) the compact-open topology. It is shown that τ C ( X ) n χ C ( X ) rt X = max ( L ( X ) , L ( X ) def X ) , where: τ is tightness; n χ is the network character; L ( X ) is the Lindel"of number. For example, it follows that, for X Čech-complete, τ C ( X ) = L ( X ) . The (apparently new) cardinal functions n χ C and rt are compared with several others.

New models for the action of Hecke operators in spaces of Maass wave forms

Ian Kiming (2007)

Annales de l’institut Fourier

Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space M λ ( N ) of Maass forms with eigenvalue 1 / 4 - λ 2 on a congruence subgroup Γ 1 ( N ) . We introduce the field F λ = ( λ , n , n λ / 2 n ) so that F λ consists entirely of algebraic numbers if λ = 0 .The main result of the paper is the following. For a packet Φ = ( ν p p N ) of Hecke eigenvalues occurring in M λ ( N ) we then have that either every ν p is algebraic over F λ , or else Φ will – for some m – occur in the first cohomology of a certain space W λ , m which is a...

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