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PERCOLATIVE INGREDIENTS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0009
Subject:
Mathematics, Probability / Statistics

This chapter contains some known results on connectivity which are used later on. The notion of unicoherence of a simply-connected set is explained and extended to lattices. Peierls (counting) ... More


On (non-)local connectivity of some Julia sets

Alexandre Dezotti and Pascale Roesch

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0009
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with the question of local connectivity of the Julia set of polynomials and rational maps. It discusses when the Julia set of a rational map is considered connected but not locally ... More


Closed Sets, Open Sets (Again), Connected Spaces

Tim Maudlin

in New Foundations for Physical Geometry: The Theory of Linear Structures

Published in print:
2014
Published Online:
April 2014
ISBN:
9780198701309
eISBN:
9780191771613
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198701309.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Chapter 3 presents the definition of a closed set in the Theory of Linear Structures, which does not correspond to the definition in standard topology. An alternative and parallel definition of an ... More


Topology and Its Shortcomings

Tim Maudlin

in New Foundations for Physical Geometry: The Theory of Linear Structures

Published in print:
2014
Published Online:
April 2014
ISBN:
9780198701309
eISBN:
9780191771613
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198701309.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

Chapter 1 reviews the structure of standard topology as an axiomatic system used to implicitly define the notion of an open set. Standard definitions of continuity, connectedness, the boundary of a ... More


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