In this paper, we define a new class of PM-factorizable topological groups. A topological group G is called PM-factorizable if, for every continuous real-valued function f on G, one can find a ...perfect homomorphism p:G→L onto a metrizable topological group L and a continuous real-valued function h on L such that f=h∘p. The relations between PR-factorizable, PM-factorizable and M-factorizable topological groups are studied. Also, some new characterizations of PR-factorizable, PM-factorizable and M-factorizable topological groups are obtained.
Profinite Groups Ribes, Luis
2010, 20100213, 2014-07-30, Letnik:
40
eBook
This updated book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. This revised edition contains new results, improved proofs, ...typographical corrections, and an enlarged bibliography.
Integral geometry is a fascinating area where numerous branches of mathematics meet together. This book is concentrated around the duality and double fibration, which is realized through the ...masterful treatment of a variety of examples.
Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of ...electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.
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