Displaying similar documents to “Quotient Overrings”

Bi-quotient maps and cartesian products of quotient maps

Ernest Michael (1968)

Annales de l'institut Fourier

Similarity:

Dans ce travail, on introduit une nouvelle classe d’applications, qui semble avoir beaucoup de propriétés désirables. En particulier, cette classe permet de donner une caractérisation des applications dont le produit cartésien avec une application quotient quelconque est toujours une application quotient.

Multiplication is Discontinuous in the Hawaiian Earring Group (with the Quotient Topology)

Paul Fabel (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a naturally occuring example of a quotient map such that q × q fails to be a quotient map. With the quotient topology, this example shows π₁(X,p) can fail to be a topological group if X is locally path connected.

On some properties of quotients of homogeneous C(K) spaces

Artur Michalak (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic...

A Hilbert-Mumford criterion for SL₂-actions

Jürgen Hausen (2003)

Colloquium Mathematicae

Similarity:

Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good...

On the three-space problem and the lifting of bounded sets.

Susanne Dierolf (1993)

Collectanea Mathematica

Similarity:

We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining...