Nonstandard methods in large-scale topology
نویسندگان
چکیده
منابع مشابه
Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications
Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.
متن کاملInstitute for Mathematical Physics Nonstandard Analysis in Point{set Topology Nonstandard Analysis in Point-set Topology
We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...
متن کاملModeling the Internet's large-scale topology.
Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining several independent databases capturing the time evolution, topo...
متن کاملQuantifying the topology of large–scale structure
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density uctuations. We rst motivate this algorithm by drawing a formal distinction between two de nitions of relevant topological characteristics, based on concepts, on the one hand, from di erential topology and, on the other, from integral geometry. The former approach leads one to concentrat...
متن کاملLarge-scale topology optimization using preconditioned Krylov subspace methods with recycling
The computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis. We propose fast iterative solvers for large threedimensional topology optimization problems to address this problem. Since the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2019
ISSN: 0166-8641
DOI: 10.1016/j.topol.2019.02.015