𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A converse to the Jordan curve theorem for digital curves

✍ Scribed by Azriel Rosenfeld

Book ID
114037172
Publisher
Elsevier Science
Year
1975
Weight
90 KB
Volume
29
Category
Article
ISSN
0019-9958

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

A Jordan Curve Theorem with Respect to C
A Jordan Curve Theorem with Respect to Certain Closure Operations on the Digital Plane
✍ Josef Ε lapal πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 257 KB

The closure operations on Z Γ— Z introduced and studied in the paper generalize the Khalimsky topology, which is commonly used as a basic topological structure in digital topology nowadays. By proving a digital analogy of the Jordan curve theorem for these closure operations, we show that they are al

The coverse of the Jordan Curve Theorem
The coverse of the Jordan Curve Theorem and a characterization of planar maps
✍ Carsten Thomassen πŸ“‚ Article πŸ“… 1989 πŸ› Springer 🌐 English βš– 255 KB

We show that a compact set F in the plane R 2 is the union of boundaries of a map if and only if each point of F is on the boundary of at least two arcwise connected components of R2\F, and it is accessible from each of those components.