--- _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' ...