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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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