mathematics

Kiiti Morita

Kiiti Morita 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 Kiiti Morita rather than just read about it. In short: Kiiti Morita (森田紀一, Morita Kiichi; February 11, 1915 – August 4, 1995) was a Japanese mathematician working in algebra and topology. Morita was born in 1915 in Hamamatsu, Shizuoka Prefecture and graduated from the Tokyo Higher Normal School in 1936.

Key takeaways

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

Reference excerpt

Kiiti Morita (森田紀一, Morita Kiichi; February 11, 1915 – August 4, 1995) was a Japanese mathematician working in algebra and topology. Morita was born in 1915 in Hamamatsu, Shizuoka Prefecture and graduated from the Tokyo Higher Normal School in 1936. Three years later he was appointed assistant at the Tokyo University of Science. He received his Ph.D. from Osaka University in 1950, with a thesis in topology. After teaching at the Tokyo Higher Normal School, he became professor at the University of Tsukuba in 1951. He held this position until 1978, after which he taught at Sophia University. Morita died of heart failure in 1995 at the Sakakibara Heart Institute in Tokyo; he was survived by his wife, Tomiko, his son, Yasuhiro, and a grandson. He introduced the concepts now known as Morita equivalence and Morita duality which were given wide circulation in the 1960s by Hyman Bass in a series of lectures. The Morita conjectures on normal topological spaces are also named after him.

Publications Morita, Kiiti (1958). "Duality for modules and its applications to the theory of rings with minimum condition". Science Reports of the Tokyo Kyoiku Daigaku. Section A. 6 (150): 83–142. MR 0096700. Zbl 0080.25702. Morita, Kiiti (1962). "Paracompactness and product spaces". Fundamenta Mathematicae. 50 (3): 223–236. doi:10.4064/fm-50-3-223-236. MR 0132525. Morita, Kiiti (1964). "Products of normal spaces with metric spaces". Mathematische Annalen. 154 (4): 365–382. doi:10.1007/BF01362570. MR 0165491. S2CID 120516038. Morita, Kiiti (1977). "Some problems on normality of products of spaces". In Novák, Josef (ed.). General topology and its relations to modern analysis and algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part B. Prague: Soc. Czechoslovak Mathematicians and Physicists. pp. 296–297. MR 0482657.

References

Worked examples

Example 1 — a first encounter with Kiiti Morita

Start with the simplest possible case. Write down what Kiiti Morita 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 Kiiti Morita 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 Kiiti Morita 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 Kiiti Morita

In research: Kiiti Morita 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 Kiiti Morita 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: Kiiti Morita is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 1995 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kiiti Morita 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 Kiiti Morita in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kiiti Morita 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 Kiiti Morita out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kiiti Morita in simple terms?

Why does Kiiti Morita 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 Kiiti Morita?

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 Kiiti Morita.