The theory of compact vector fields and some of its applications to topology of functional spaces (I)

A. Granas

Displaying similar documents to “The theory of compact vector fields and some of its applications to topology of functional spaces (I)”

On the disconnection of Banach spaces

A. Granas (1960)

Fundamenta Mathematicae

Similarity:

Embedding proper homotopy types

M. Cárdenas, T. Fernández, F. F. Lasheras, A. Quintero (2003)

Colloquium Mathematicae

Similarity:

We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in $ℝ^{2 n - c}$ (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite...

There are no Phantom Pairs of Mappings to 1-Dimensional CW-Complexes

Sibe Mardešić (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

Two mappings from a CW-complex to a 1-dimensional CW-complex are homotopic if and only if their restrictions to finite subcomplexes are homotopic.

Fixed point and homotopy result for mappings satisfying an implicit relation

I. Altun, D. Turkoglu (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

In this paper, we prove some fixed point theorems for single valued mappings satisfying an implicit relation on space with two metrics. In addition we give a homotopy result using our theorems.

G-ANR's with homotopy trivial fixed point sets

Sergey A. Antonyan (2007)

Fundamenta Mathematicae

Similarity:

Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set $X^{H}$ is homotopy trivial for each closed subgroup H ⊂ G.

Gradient homotopies of gradient vector fields

A. Parusiński (1990)

Studia Mathematica

Similarity:

Set theoretical approach to the disconnection theory of the Euclidean space

Karol Borsuk (1950)

Fundamenta Mathematicae

Similarity:

On the homotopy type of $Diff (M^{n})$ and connected problems

Dan Burghelea (1973)

Annales de l'institut Fourier

Similarity:

This paper reports on some results concerning: a) The homotopy type of the group of diffeomorphisms $Diff (M^{n})$ of a differentiable compact manifold $M^{n}$ (with $C^{\infty}$ -topology). b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo $M^{n}$ (with $C^{o}$ -topology). As a biproduct, one gets new facts about the homotopy groups of $Diff (D^{n}, \partial D^{n}), {Top}_{n}$ , ${Top}_{n} / O_{n}$ and about the number of connected components of the space of topological and combinatorial pseudoisotopies. ...

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Josef Janyška (2001)

Archivum Mathematicum

Similarity:

Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$ . We classify all natural (in the sense of [KMS]) 0-order vector fields and 2-vector fields on $T M$ generated by $g$ and $K$ . We get that all natural vector fields are of the form $E (u) = α (h (u)) u^{H} + β (h (u)) u^{V},$ where $u^{V}$ is the vertical lift of $u \in T_{x} M$ , $u^{H}$ is the horizontal lift of $u$ with respect to $K$ , $h (u) = 1 / 2 g (u, u)$ and $α, β$ are smooth real functions defined on $R$ . All natural 2-vector fields are of the form $Λ (u) = γ_{1} (h (u)) Λ (g, K) + γ_{2} (h (u)) u^{H} \land u^{V},$ where $γ_{1}$ , $γ_{2}$ are smooth real functions...

On the Stark-Shintani units and the ideal class groups in the cyclotomic $ℤ_{p}$ -extensions of class fields over real quadratic fields

Tsuyoshi Itoh (2002)

Acta Arithmetica

Similarity:

Topological degree for ultimately compact multivalued vector fields in topological vector spaces

Lj. Gajić (1987)

Matematički Vesnik

Similarity:

Cohomotopy groups and shape in the sense of Fox

Stanisław Godlewski (1972)

Fundamenta Mathematicae

Similarity:

Some results on homotopy theory of modules

Zheng-Xu He (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di $i$ -omotopia per moduli ed omomorfismi di moduli.