Concept
First-countable space
Related publications (10)
Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
San Diego2023Property FW, differentiable structures and smoothability of singular actions
We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group Gamma has the fixed point property FW for walls (for example, if it has property(T)), every aperiodic action of Gamma by diffe ...
WILEY2020A lower bound on opaque sets
It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...
ELSEVIER SCIENCE BV2019A pathwise approach to the extinction of branching processes with countably many types
We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is then used to sho ...
ELSEVIER SCIENCE BV2019Topological Structures on DMC spaces
Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. We s ...
2017Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
Fabio Nobile, Lorenzo Tamellini
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...
2016Numerical Approximation of Flows in Random Porous Media
The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...
EPFL2016MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity
Fabio Nobile, Lorenzo Tamellini
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a ...
MATHICSE2015Moyennabilité et courbure
As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...
EPFL2010Manganese doped ZnS nanoparticles
Nanostructured materials can be defined as those materials whose structural elements - clusters, crystallites or molecules - have dimensions in the 1-100 nm range. The explosion in both academic and industrial interest over the past 20 years arises from th ...
EPFL2004