Some topological extensions of plane geometry
Let A be a closed subset of the plane. For a point b in the plane whose distance to A is d(b,A) let S(b,A) = {z : |z-b| d (b,A)}. Let E(A) be the set of points e for which S(b,A) ∩ A has at least two points. Let f(A) be the set of open intervals (a,b) for which there is an e ℇ E(A) and a component o...
- Autores:
-
Bell, H.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1975
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42429
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42429
http://bdigital.unal.edu.co/32526/
- Palabra clave:
- Plane geometry
topological extensions
closed subset
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Let A be a closed subset of the plane. For a point b in the plane whose distance to A is d(b,A) let S(b,A) = {z : |z-b| d (b,A)}. Let E(A) be the set of points e for which S(b,A) ∩ A has at least two points. Let f(A) be the set of open intervals (a,b) for which there is an e ℇ E(A) and a component of S(e,A)-A with endpoints a and b. The sets E(A) and f(A) are the central tools in this paper. |
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