Pseudo-measures supported by totally disconnected sets

1971 ◽  
pp. 20-45
Author(s):  
John Benedetto
Keyword(s):  
Totally Disconnected ◽  
Disconnected Sets

scholarly journals ON THE CLASSIFICATION OF FRACTAL SQUARES

Fractals ◽  
2016 ◽  
Vol 24 (01) ◽  
pp. 1650008 ◽  
Author(s):  
JUN JASON LUO ◽  
JING-CHENG LIU
Keyword(s):  
Topological Structure ◽  
Totally Disconnected ◽  
Disconnected Sets

In the previous paper [K. S. Lau, J. J. Luo and H. Rao, Topological structure of fractal squares, Math. Proc. Camb. Phil. Soc. 155 (2013) 73–86], Lau, Luo and Rao completely classified the topological structure of so called fractal square [Formula: see text] defined by [Formula: see text], where [Formula: see text]. In this paper, we further provide simple criteria for the [Formula: see text] to be totally disconnected, then we discuss the Lipschitz classification of [Formula: see text] in the case [Formula: see text], which is an attempt to consider non-totally disconnected sets.

scholarly journals Plane continua and totally disconnected sets of buried points

2011 ◽  
Vol 140 (1) ◽  
pp. 351-356
Author(s):  
Jan van Mill ◽  
Murat Tuncali
Keyword(s):  
Totally Disconnected ◽  
Disconnected Sets

scholarly journals The hyperspace of totally disconnected sets

2020 ◽  
Vol 55 (1) ◽  
pp. 113-128
Author(s):  
Raúl Escobedo ◽  
◽  
Patricia Pellicer-Covarrubias ◽  
Vicente Sánchez-Gutiérrez ◽  
◽  
...  
Keyword(s):  
Totally Disconnected ◽  
Disconnected Sets

scholarly journals A note on the removability of totally disconnected sets for analytic functions

2020 ◽  
Vol 72 (3) ◽  
pp. 425-426
Author(s):  
A. V. Pokrovskii
Keyword(s):  
Imaginary Part ◽  
Complex Plane ◽  
Analytic Functions ◽  
Closed Subset ◽  
The Real ◽  
Totally Disconnected ◽  
Disconnected Sets

UDC 517.537.38 We prove that each totally disconnected closed subset E of a domain G in the complex plane is removable for analytic functions f ( z ) defined in G ∖ E and such that for any point z 0 ∈ E the real or imaginary part of f ( z ) vanishes at z 0 .  

scholarly journals Compact, totally disconnected sets that contain $K$-sets.

1975 ◽  
Vol 21 (4) ◽  
pp. 315-319
Author(s):  
Frank B. Miles
Keyword(s):  
Totally Disconnected ◽  
Disconnected Sets

scholarly journals Complete regularity of Ellis semigroups of -actions

2020 ◽  
pp. 1-17
Author(s):  
MARCY BARGE ◽  
JOHANNES KELLENDONK
Keyword(s):  
Complete Regularity ◽  
Completely Regular ◽  
Ellis Semigroup ◽  
Totally Disconnected

Abstract It is shown that the Ellis semigroup of a $\mathbb Z$ -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$ - or $\mathbb R$ -action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

scholarly journals Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 971
Author(s):  
Oded Shor ◽  
Felix Benninger ◽  
Andrei Khrennikov
Keyword(s):  
Experimental Data ◽  
Clustering Algorithms ◽  
Realistic Model ◽  
Minkowski Geometry ◽  
Ultrametric Spaces ◽  
Chsh Inequality ◽  
Classical Quantum ◽  
Basic Features ◽  
Totally Disconnected ◽  
Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.

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