Partial Partitions, Partial Connections and Connective Segmentation

Ronse, Christian

doi:10.1007/s10851-008-0090-5

Cited by 62 publications

(150 citation statements)

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“…Note also that the point z does not belong to any component of Y since there is no connected substar of Y that contains z. In fact, the definition of connected component adopted in this paper falls into the category of partial connections, which are investigated by C. Ronse in [50], and which do not require that any element of a set belongs to a connected component of this set. This second example also illustrates our choice of considering the notion of d-path (with d = n) for the connectivity of the complement of the simplicial complexes (i.e.…”

Section: ) By Definition Cmentioning

confidence: 99%

Collapses and Watersheds in Pseudomanifolds of Arbitrary Dimension

et al. 2014

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Section: ) By Definition Cmentioning

confidence: 99%

Collapses and Watersheds in Pseudomanifolds of Arbitrary Dimension

et al. 2014

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“…Since P ⊆ Q[P ] for all P ⊆ Q, we have As shown in [26], there is a bijection between the "partial connections" of [21] and separation spaces satisfying (S0), (S1), (S2), (SR0), (SR1), and (SR2). Equivalent constructions have been considered e.g.…”

Section: Lemma 412 Suppose (P) Holds Then (M) Is Equivalent To (G)mentioning

confidence: 99%

Oriented components and their separations

Stadler

2017

Appl. Gen. Topol.

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There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces.2010 MSC: 54D05; 54E05.

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“…A partition π(S) associated with a set S ∈ P(E) is called partial partition of E of support S [9]. The partial partition of S in the single class S is denoted by {S}.…”

Section: Hierarchies Of Partial Partitionsmentioning

confidence: 99%