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PointfreeTopology

Next door

Other legends
and related ideas

Pointfree topology never worked in isolation. Its questions were sharpened by people working next door — on rings of functions, on ordered algebra — whose ideas it borrowed, answered and rebuilt without points.

  1. Melvin Henriksen

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    1927–2009 · Purdue · Harvey Mudd

    Rings of continuous functions

    Helped turn C(X), the ring of continuous real functions on a space, into a subject of its own — the algebra that the pointfree theory of C(L) later rebuilt without points.

  2. Jorge Martínez

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    1945–2020 · University of Florida

    Algebraic frames

    Came to frames from lattice-ordered groups, and made the algebraic frames — those generated by their compact elements — a working tool for both subjects.

More to come

This list is only a start

Many more people and ideas sit on the border of the subject — quantales and noncommutative topology, uniform and metric frames, formal topology and constructive mathematics, domain theory and the logic of observable properties, topos theory, lattice-ordered rings. Each has its own legends, and each would deserve a page here.

If there is someone you think belongs on this page, or an idea you would like to see written up, get in touch.