Construct · 1 fields · 2 citations

atlas: a standalone construct

One name. One construct. A landmark on the map.

● anchor · a standalone construct Nearest construct by meaningmanifoldcompare the meanings
How to read this

Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to atlas is manifold.

Hold this as a prompt, not a verdict. Two constructs sitting close in meaning is a reason to read them side by side and decide for yourself whether they are one idea under two names. It is not proof that they are. Compare the meanings in the Collider.

atlas1 CONSTRUCTAtlas of chartsWEYL · CHART ATLAS

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Differential geometry

A collection of coordinate charts on a manifold

A collection of coordinate charts that together cover a manifold, an abstract space that looks locally like ordinary flat space. Each chart maps a patch of the space to coordinates, and where patches overlap the charts agree through smooth transition rules. Weyl's Die Idee der Riemannschen Fläche (1913) introduced the idea of describing a surface by local coordinate patches, and Whitney's Differentiable manifolds (1936) formalised the modern manifold as a space carrying a consistent family of overlapping charts. The word borrows directly from map-making, since a set of charts covering a space resembles a book of maps covering the earth, but the referent is a purely mathematical object, not a printed volume or a bone in the neck.[1][2]

Unit
One indexed family of overlapping charts covering a given manifold
Recovery means
Not applicable
Measured by
Specified by its charts, their coordinate domains, and the transition maps that relate overlapping charts

Next

Run it through the Collider, or take the citations with you.

See how atlas sits against neighbouring constructs in the Collider, or export every reference on this page in one click.

Open in ColliderExport BibTeXReport this entry

Nearby constructs

manifold2 fields · 2 citationsjingle · one word, two constructstopology4 fields · 6 citationsjingle · one word, four constructsaxis1 fields · 1 citationsanchor · a standalone construct

References

  1. Weyl, H. (1913). Die Idee der Riemannschen Fläche. B. G. Teubner.
  2. Whitney, H. (1936). Differentiable manifolds. Annals of Mathematics, 37(3), 645–680. https://doi.org/10.2307/1968482

Cited on this page?

Confirm your construct, or correct us.

If your work is cited behind one of these entries, you know better than we do whether we captured the meaning right. Confirm it, suggest an edit, or dispute it, and your name goes on the entry as an author who has checked it, linked to your ORCID.

Claim your construct