---
_id: '4023'
abstract:
- lang: eng
text: Let B be a finite pseudodisk collection in the plane. By the principle of
inclusion-exclusion, the area or any other measure of the union is [GRAPHICS]
We show the existence of a two-dimensional abstract simplicial complex, X subset
of or equal to 2(B), so the above relation holds even if X is substituted for
2(B). In addition, X can be embedded in R(2) SO its underlying space is homotopy
equivalent to int Boolean OR B, and the frontier of X is isomorphic to the nerve
of the set of boundary contributions.
acknowledgement: Supported by the National Science Foundation, under Grant ASC-9200301
and the Alan T. Waterman Award CCR-9118874.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Edgar
full_name: Ramos, Edgar
last_name: Ramos
citation:
ama: Edelsbrunner H, Ramos E. Inclusion-exclusion complexes for pseudodisk collections.
Discrete & Computational Geometry. 1997;17(3):287-306. doi:10.1007/PL00009295
apa: Edelsbrunner, H., & Ramos, E. (1997). Inclusion-exclusion complexes for
pseudodisk collections. Discrete & Computational Geometry. Springer.
https://doi.org/10.1007/PL00009295
chicago: Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes
for Pseudodisk Collections.” Discrete & Computational Geometry. Springer,
1997. https://doi.org/10.1007/PL00009295.
ieee: H. Edelsbrunner and E. Ramos, “Inclusion-exclusion complexes for pseudodisk
collections,” Discrete & Computational Geometry, vol. 17, no. 3. Springer,
pp. 287–306, 1997.
ista: Edelsbrunner H, Ramos E. 1997. Inclusion-exclusion complexes for pseudodisk
collections. Discrete & Computational Geometry. 17(3), 287–306.
mla: Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for
Pseudodisk Collections.” Discrete & Computational Geometry, vol. 17,
no. 3, Springer, 1997, pp. 287–306, doi:10.1007/PL00009295.
short: H. Edelsbrunner, E. Ramos, Discrete & Computational Geometry 17 (1997)
287–306.
date_created: 2018-12-11T12:06:30Z
date_published: 1997-04-01T00:00:00Z
date_updated: 2022-08-18T14:39:39Z
day: '01'
doi: 10.1007/PL00009295
extern: '1'
intvolume: ' 17'
issue: '3'
language:
- iso: eng
month: '04'
oa_version: None
page: 287 - 306
publication: Discrete & Computational Geometry
publication_identifier:
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2104'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inclusion-exclusion complexes for pseudodisk collections
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 17
year: '1997'
...