File:Refinement on a planar shape.svg

Original file (SVG file, nominally 378 × 737 pixels, file size: 9 KB)

Summary

Description
English: Below left: Refinement of the cover so that no point in the shape is contained in more than 3 sets.

Below right: An attempt to refine the cover so that no point in the shape would be contained in more than 2 sets. Notice how some set border intersection points cannot be covered.

Purpose: To illustrate the role of covers in the definition of topological dimension
Date
Source Own work
Author Ian Remsen

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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illustration of covers in topological dimension

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7 February 2023

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Date/TimeThumbnailDimensionsUserComment
current04:50, 8 February 2023Thumbnail for version as of 04:50, 8 February 2023378 × 737 (9 KB)RemsenseUploaded own work with UploadWizard

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