101

Baire Category Theorem for Locally Compact Spaces

States and proves the standard Baire category theorem without using the concept of category and states and proved an analogue in the context of locally compact Hausdorff spaces.

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M.Sc.
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(Downloaded 1502 times last on 11 January 2025, 04:03 am

103

The Role of LUB Axiom in Real Analysis

Brings out the role of LUB property (order completeness) of $R$. Gives a unified view of many of the crucial results in a first course in real analysis

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likely to be best for a review of basic real analysis.
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(Downloaded 2966 times last on 11 January 2025, 03:19 pm

105

Maurer-Cartan Forms and Rigidity for Space Curves

This is a section in frenet.pdf

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may be kept as a separate article
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(Downloaded 528 times last on 06 January 2025, 11:00 pm

107

Minkowski Inequality

A subconvexity argument to give a direct proof of Minkowski inequality

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M.Sc.
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(Downloaded 499 times last on 08 January 2025, 12:07 pm

109

Miscellaneous Results in Analysis

This article is a collection of results with possibly cute proofs. As I gathered them, I wrote them up lest that I forget such arguments!

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B.Sc
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(Downloaded 1035 times last on 10 January 2025, 03:36 pm

111

An Outline of Module Theory

An outline module theory leading up to the structure theorem of FG modules over a Euclidean domain and its two standard applications (FGA groups and canonical forms.)

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M.Sc.
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(Downloaded 818 times last on 10 January 2025, 04:56 pm

113

A Conceptual Introduction to Several Variable Calculus

A conceptual introduction to differential calculus of several variables. Weans away the students from mindless computations and introduces them to a single (geometric) trick which is employed in the proofs of the most of the results. Also, brings out the geometric meaning of the partial derivatives.

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Final year B.Sc, M.Sc
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(Downloaded 2295 times last on 11 January 2025, 03:20 pm

115

Nested Interval Theorem and Its Applications

Proves the nested interval theorem and gives its applications such as intermediate value theorem, Heine-Borel theorem, Bolzano-Weierstrass theorem, extreme value theorem. Also gives two unusual applications: density of rationals and Volterra's proof of nonexistence of a function which is continuous at rationals and discontinuous at irrationals.

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B.Sc./M.Sc
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(Downloaded 2743 times last on 11 January 2025, 10:46 am

117

Additive Homomorphisms of R and Nonmeasurable Sets

Existence of a nonmeasurable subset of $R$ using additive homomorphisms of $R$ and regularity of the Lebesgue measure.

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M.Sc./Ph.D
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(Downloaded 533 times last on 08 January 2025, 12:08 pm

119

Examples of Complete ON Bases in Hilbert Spaces

Examples of complete orthonormal basis of some Hilbert spaces of functions

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it teaches good analysis and makes the `traditional' functional analysis course more analytic.
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(Downloaded 556 times last on 08 January 2025, 12:08 pm