---
_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.
    <i>Discrete &#38; Computational Geometry</i>. 1997;17(3):287-306. doi:<a href="https://doi.org/10.1007/PL00009295">10.1007/PL00009295</a>
  apa: Edelsbrunner, H., &#38; Ramos, E. (1997). Inclusion-exclusion complexes for
    pseudodisk collections. <i>Discrete &#38; Computational Geometry</i>. Springer.
    <a href="https://doi.org/10.1007/PL00009295">https://doi.org/10.1007/PL00009295</a>
  chicago: Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes
    for Pseudodisk Collections.” <i>Discrete &#38; Computational Geometry</i>. Springer,
    1997. <a href="https://doi.org/10.1007/PL00009295">https://doi.org/10.1007/PL00009295</a>.
  ieee: H. Edelsbrunner and E. Ramos, “Inclusion-exclusion complexes for pseudodisk
    collections,” <i>Discrete &#38; Computational Geometry</i>, vol. 17, no. 3. Springer,
    pp. 287–306, 1997.
  ista: Edelsbrunner H, Ramos E. 1997. Inclusion-exclusion complexes for pseudodisk
    collections. Discrete &#38; Computational Geometry. 17(3), 287–306.
  mla: Edelsbrunner, Herbert, and Edgar Ramos. “Inclusion-Exclusion Complexes for
    Pseudodisk Collections.” <i>Discrete &#38; Computational Geometry</i>, vol. 17,
    no. 3, Springer, 1997, pp. 287–306, doi:<a href="https://doi.org/10.1007/PL00009295">10.1007/PL00009295</a>.
  short: H. Edelsbrunner, E. Ramos, Discrete &#38; 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'
fulldoi: https://doi.org/10.1007/PL00009295
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'
...