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Definable one dimensional topologies in o-minimal structures
[article]
2019
arXiv
pre-print
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We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space (X,τ) is definably homeomorphic to an affine ...
definable space (namely, a definable subset of M^n with the induced subspace topology). ...
Introduction The goal of this article is to study definable one-dimensional Hausdorff topologies in o-minimal structures, and to understand when they are definably homeomorphic to a definable set in some ...
arXiv:1807.08086v2
fatcat:cj6af5pk7zauhplz2y2cslcyju
Topology of definable abelian groups in o-minimal structures
2011
Bulletin of the London Mathematical Society
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In this note we show that every definably connected, definably compact abelian definable group in an o-minimal expansion of a real closed field of dimension not 4 is definably homeomorphic to a torus of ...
Moreover, in the semialgebraic case the result holds for all dimensions. ...
Wall for their comments concerning low dimensional topology and classification of manifolds. ...
doi:10.1112/blms/bdr108
fatcat:yfadeen2mvac3a53zr2tvfguw4
Taming the Landscape of Effective Theories
[article]
2021
arXiv
pre-print
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are definable using the tame geometry built from an o-minimal structure. ...
In particular, we will exploit the fact that coset spaces and period mappings are definable in an o-minimal structure and argue for non-trivial tameness results in higher-supersymmetric theories and in ...
The basic strategy in defining a tame topology based on o-minimal structures [7] is to specify
the space of allowed subsets of Rn , for every n. ...
arXiv:2112.08383v1
fatcat:knzm6u3bzzfldm6j6ugf4pytne
Page 575 of Mathematical Reviews Vol. , Issue 93b
[page]
1993
Mathematical Reviews
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In the case of a two-dimensional definably connected group definable in an o-minimal structure, the structure theorem goes via the facts that such a group is solvable and has a normal one- dimensional ...
Let G be a three-dimensional nonsolvable definably connected group which is definable in an o-minimal structure M. ...
LEAST STRATIFICATIONS AND CELL-STRUCTURED OBJECTS IN GEOMETRIC MODELLING
2002
International journal of shape modeling
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The main contribution of the paper is an existence proof for least stratifications (of sets in O-minimal structures). ...
Results from the study of O-minimal structures are used to formalise fundamental objects and operations for geometric modelling kernels. ...
The proof depends on cellular decomposition results for O-minimal structures. The next section formally defines O-minimal structures, Icells and the decomposition of definable sets. ...
doi:10.1142/s0218654302000054
fatcat:3axydiciizf4xn5mkdbhmvvsce
Tame Complex Analysis and o-minimality
2011
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
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O-minimal structures offer a tame setting for various areas of mathematics. Some features: Topology: Order topology on R and product topology on R n . ...
From now on: We work in the structure R an,exp . A torus means a one-dimensional torus. In the structure R an,exp : Let A t , t ∈ T , be a definable family of g-dimensional abelian varieties over C. ...
doi:10.1142/9789814324359_0040
fatcat:egznsme3dnh4ljajhkn2qlaruq
Zero-groups and maximal tori
[article]
2005
arXiv
pre-print
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We give a presentation of various results on zero-groups in o-minimal structures together with some new observations. ...
In particular we prove that if G is a definably connected definably compact group in an o-minimal expansion of a real closed field, then for any maximal definably connected abelian subgroup T of G, G is ...
in the o-minimal structure (R, <, +, ·). ...
arXiv:math/0511162v1
fatcat:7o3r6zxshfdsxjb5nc3akrgsiq
Three-dimensional stress-based topology optimization using SIMP method
2019
International Journal for Simulation and Multidisciplinary Design Optimization
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Structural topology optimization problems have been formulated and solved to minimize either compliance or weight of a design domain under volume or stress constraints. ...
The introduction of threedimensional analysis is a more realistic approach to many applications in industry and research, but most of the developments in stress-based topology optimization are two-dimensional ...
The developments in structural optimization that uses SIMP method focus on two-dimensional problems and those that are formulated for three-dimensional problems consider a compliance minimization problem ...
doi:10.1051/smdo/2019005
fatcat:lshyb4oj2jabrlbznlknqzfcfu
One Dimensional T.T.T Structures
[article]
2012
arXiv
pre-print
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In this paper we analyze the relationship between o-minimal structures and the notion of \omega -saturated one dimensional t.t.t structures. ...
As a corollary we obtain the result that if an \omega -saturated one dimensional t.t.t structure admits a topological group structure then it is locally o-minimal. ...
I'd like to thank Ehud Hrushovski for providing valuable insights and guidance throughout the time spent working on this paper. ...
arXiv:1210.5603v1
fatcat:g4m6jjjmyrghrhel3ar5phj4v4
Aspects in topology-based geometric modeling Possible tools for discrete geometry?
[chapter]
1997
Lecture Notes in Computer Science
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Topology-based Geometric Modeling is concerned with modeling subdivisions of geometric spaces. Methods are close to that of combinatorial topology, but for different purposes. ...
construction operations can be easily defined on these structures. ...
Topological properties are defined on semi-simplicial sets and can be extended on generalized maps. ...
doi:10.1007/bfb0024828
fatcat:c3knhescqvdafc6edvqyv35zgi
Groups and rings definable in d-minimal structures
[article]
2021
arXiv
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We study groups and rings definable in d-minimal expansions of ordered fields. We generalize to such objects some known results from o-minimality. ...
In particular, we prove that we can endow a definable group with a definable topology making it a topological group, and that a definable ring of dimension at least 1 and without zero divisors is a skew ...
Pillay ([Pil88] ) proved that every group definable in an o-minimal structure can be endowed with a definable topology that makes it both a topological group and a definable manifold. ...
arXiv:1205.4177v2
fatcat:7kvkr4sxybfbxoomrnwdlhc2vq
Compactness and connectedness in topological groups
1998
Topology and its Applications
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(b) q(G) = 1, (c) G is zero-dimensional; in particular, always c(G) = q(G) for such a group G. ...
We also discuss the role of connectedness for the question when topology or algebra alone determine the topological group structure of a compact-like group. 0 1998 Elsevier Science B.V. ...
Wiegandt, Connectedness and disconnectedness in topology, Gen. Topology Appl. 5 (197.5) 137-154. [2] A. Arkhangel'skii, Mappings connected with topological groups, Dokl. Akad. Nauk SSSR ...
doi:10.1016/s0166-8641(97)00094-1
fatcat:77rbdmpbvzfnhpzmt5jkc223ke
Affiness of topological space definable in a definably complete uniformly locally o-minimal structure of the second kind
[article]
2021
arXiv
pre-print
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We give a necessary and sufficient condition for a one-dimensional regular and Hausdorff topological space definable in a definably complete uniformly locally o-minimal structure of the second kind having ...
definable bounded multiplication being affine. ...
Rosel gave a necessary and sufficient condition for a one-dimensional topological space with a topology definable in an o-minimal structure being affine in [9] when the definable set in consideration ...
arXiv:2110.15616v1
fatcat:e3zynktrlnhhrowm3d3aupr24m
Book Review: Tame topology and o-minimal structures
2000
Bulletin of the American Mathematical Society
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Tame topology and o-minimal structures, by Lou van den Dries, Cambridge Univ. ...
Speissegger [18] extended this by showing that the "Pfaffian closure" of an o-minimal structure is o-minimal. §4 The book Van den Dries' Tame topology and O-minimal structures can be viewed as a compelling ...
doi:10.1090/s0273-0979-00-00866-1
fatcat:p5tpkcjbfbay5pzyu6ieajpqmq
Spacetime granularity from finite-dimensionality of local observable algebras
[article]
2019
arXiv
pre-print
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Motivated by these ideas, we show that operational spacetime topology is described by an atomistic Boolean algebra if (i) local observable algebras are finite-dimensional factors, (ii) the intersection ...
Thus, in this case, spacetime has a point-free granular behavior at small scales. ...
Acknowledgments I thank Paolo Bertozzini, Philipp Höhn and Ted Jacobson for enlightening discussions and helpful comments on an earlier version of the manuscript. ...
arXiv:1908.09293v3
fatcat:fvfbvvfumnhnbbj6nuxqdnhchq
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