scholarly journals Totally disconnected sets, Jordan curves, and conformal maps

1972 ◽  
Vol 2 (1-4) ◽  
pp. 15-19 ◽  
Author(s):  
G. Piranian
Keyword(s):  
Conformal Maps ◽  
Jordan Curves ◽  
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.

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

2021 ◽  
Vol 179 (1) ◽  
pp. 59-74
Author(s):  
Josef Šlapal
Keyword(s):  
Direct Product ◽  
Jordan Curve ◽  
Closure Operator ◽  
Jordan Curve Theorem ◽  
Closure Operators ◽  
Ternary Relation ◽  
Digital Space ◽  
Jordan Curves ◽  
Curves And Surfaces ◽  
Digital Plane

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

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