mathematics

Hing Tong

Hing Tong is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hing Tong rather than just read about it. In short: Hing Tong (16 February 1922 – 4 March 2007) was an American mathematician. He is well known for providing the original proof of the Katetov–Tong insertion theorem.

Key takeaways

Hing Tong belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hing Tong to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hing Tong from memory before moving on to harder problems.

Reference excerpt

Hing Tong (16 February 1922 – 4 March 2007) was an American mathematician. He is well known for providing the original proof of the Katetov–Tong insertion theorem.

Life Hing Tong was born in Canton, China. He received his bachelor's degree from the University of Pennsylvania. In 1947, he received his doctorate in mathematics from Columbia University, where his thesis advisor was Edgar Lorch. In 1956, he married fellow mathematician, Mary Powderly. He was the father of five children.

Work Hing Tong made many significant contributions to the area of algebraic topology, and served in a number of academic capacities. In 1947, after receiving a National Research Council fellowship, he became an assistant professor at Barnard College (Columbia University). In 1955, he was a visiting scholar at the Institute for Advanced Study in Princeton. Also in 1955, he was appointed professor of mathematics (and eventually chairman of the mathematics department) at Wesleyan University. He later became a professor of mathematics at Fordham University, where he also served as chairman of the department. He was listed among the Outstanding Educators of America in 1973. Tong retired from academia in 1984 to concentrate on research in theoretical physics. A commemorative brick in the Paul Halmos Commemorative Walk at the Carriage House Conference Center of the Mathematical Association of America (MAA) in Washington, DC, reads: "Hing Tong, Topology and Physics".

Important publications Hing Tong, "The elements of the theory of transfinite numbers", Columbia University masters dissertation: 1944. Hing Tong, "On Ideals Associated with Certain Normed Rings over Topological Spaces", Columbia University Ph.D. dissertation: 1947. Hing Tong, "On Some Problems of Cech", The Annals of Mathematics, 2nd Series, Vol. 50, No. 1: January, 1949, pp. 154–157. Hing Tong, "On Ideals of Certain Topologized Rings of Continuous Mappings Associated with Topological Spaces", The Annals of Mathematics, 2nd Series, Vol. 50, No. 2: April, 1949, pp. 329–340. Hing Tong, "Some characterizations of normal and perfectly normal spaces", Duke Math. J. Volume 19, Number 2: 1952, pp. 289–292. Mary Powderly and Hing Tong, "On Orbital Topologies[link removed]", The Quarterly Journal of Mathematics, 7(1), 1956: pp. 1–2. George Kozlowski and Hing Tong, "Two problems of Hewitt on topological expansions", Duke Math. J. Volume 33, Number 3: September, 1966, pp. 475–476. Edgar Lorch and Hing Tong, "Continuity of Baire Functions and Order of Baire Sets", Indiana University Mathematics Journal, 16: 1967, pp. 991–995. Edgar Lorch and Hing Tong, "A Completeness Theorem on the Group of Baire Equivalences", Indiana University Mathematics Journal, 19: 1970, pp. 189–193. Hing Tong, "Non-existence of certain topological expansions", Annali di Matematica Pura ed Applicata, Volume 86, Number 1: December, 1970, pp. 43–45. Hing Tong, "Solutions of problems of P. S. Alexandroff on extensions of topological spaces", Annali di Matematica Pura ed Applicata, Volume 86, Number 1: December, 1970, pp. 47–51. Edgar Lorch and Hing Tong, "Compactness, metrizability, and Baire isomorphism", Acta Sci. Math. (Szeged) 35: 1973. Edgar Lorch and Hing Tong, "On the automorphisms of certain groups of permutations", Bulletin of the Institute of Mathematics Academia Sinica, Volume 2, Number 2: 1974. Mary Powderly, Hing Tong, and George Kozlowski, "On a problem of Alexandroff and Hopf", Bulletin of the Institute of Mathematics Academia Sinica, Volume 3, Number 1: 1975. Edgar Lorch and Hing Tong, "Baire isomorphisms between certain non-metric spaces", Annali di Matematica Pura ed Applicata, Volume 103, Number 1: December, 1975. Edgar Lorch and Hing Tong, "On the automorphisms of the group of Baire equivalences of a complete separable metric space", Bulletin of the Institute of Mathematics Academia Sinica, Volume 6, Number 2: 1978.

External links Hing Tong in the Mathematical Genealogy project

Notes

Illustrations

Worked examples

Example 1 — a first encounter with Hing Tong

Start with the simplest possible case. Write down what Hing Tong claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hing Tong before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hing Tong ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hing Tong

In research: Hing Tong appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hing Tong in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hing Tong is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1922 births, 2007 deaths, American topologists, so understanding it makes those chapters shorter.
In everyday life: Look for Hing Tong outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hing Tong in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hing Tong means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hing Tong out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hing Tong in simple terms?

Hing Tong (16 February 1922 – 4 March 2007) was an American mathematician. He is well known for providing the original proof of the Katetov–Tong insertion theorem.

Why does Hing Tong matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hing Tong?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hing Tong.