Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Lešnik, Davorin"'
Autor:
Lešnik, Davorin
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are continuou
Externí odkaz:
http://arxiv.org/abs/2104.10399
Autor:
Kalisnik, Sara, Lesnik, Davorin
A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in a Euclide
Externí odkaz:
http://arxiv.org/abs/2006.09194
Autor:
Kališnik, Sara, Lešnik, Davorin
The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The result does not
Externí odkaz:
http://arxiv.org/abs/1801.08882
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional non-linear
Externí odkaz:
http://arxiv.org/abs/1701.08395
The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max, +), Izhakian-Rowen's e
Externí odkaz:
http://arxiv.org/abs/1607.00245
Autor:
Kališnik, Sara, Lešnik, Davorin
Publikováno v:
In Journal of Symbolic Computation March-April 2021 103:280-299
Autor:
Lešnik, Davorin
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to reflectio
Externí odkaz:
http://arxiv.org/abs/1402.6645
Autor:
Kališnik, Sara, Lešnik, Davorin
Publikováno v:
In Journal of Symbolic Computation July-August 2019 93:100-119
Publikováno v:
In Advances in Applied Mathematics January 2019 102:113-142
Autor:
Lešnik, Davorin
The Urysohn space is a complete separable metric space, universal among separable metric spaces for extending finite partial isometries into it. We present an alternative construction of the Urysohn space which enables us to show that extending isome
Externí odkaz:
http://arxiv.org/abs/1201.2077