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Found total 224 results. Displaying results from 21 to 40.

 
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21
Noncontractibility of the Circle

Non-contractibility of the circle and Brouwer Fixed point theorem in $R^2$. Proofs are analytic in nature, as we classify the functions into punctured plane.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1366 times last on 25 April 2025, 10:07 pm
22
Simple and Direct Proofs of Some Results in the Theory of Compact Spaces

Simple and direct proofs of some results in the theory of compact spaces.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 2105 times last on 26 April 2025, 06:48 am
23
Compact Metric Spaces

Give equivalent conditions for a metric space to be compact

Keywords :

Final year BSc, 1st year MSc
MTTS Level :
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(Downloaded 1566 times last on 25 April 2025, 10:07 pm
24
Compact Spaces

Proves Heine-Borel theorems in $R$, $R^n$ and Tykonoff's theorem.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1012 times last on 25 April 2025, 10:07 pm
25
Properties Equivalent to the LUB Property of Ordered Fields

Properties equivalent to LUB property. Almost similar to the article ?complete1.pdf? but contains an example of complete non-Archimedean field.

Keywords :

Final year B.Sc,, M.Sc.
MTTS Level :
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(Downloaded 2318 times last on 26 April 2025, 07:59 am
26
Properties Equivalent to the LUB Property of Ordered Fields

Properties equivalent to LUB property. Almost similar to the article ?complete.pdf?, but contains more details but excludes an example of complete non-Archimedean field.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1709 times last on 25 April 2025, 10:07 pm
27
A Diagnostic Quiz in Complex Analysis

A diagnostic quiz in complex analysis.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 1574 times last on 26 April 2025, 12:33 pm
28
Complex Analysis: Handout-1 (Basic Calculus on C)

A handout dealing with limits, differentiation of functions from $R$ to $C$, from 4C$ to $C$ and integartion of $C$-valued continuous funtions on $[a,b]$.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1391 times last on 25 April 2025, 10:07 pm
29
Complex Analysis: Handout-2 (Results on Power Series)

Results on power series

Keywords :


MTTS Level :
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(Downloaded 2081 times last on 25 April 2025, 10:07 pm
30
Complex Analysis: Handout-3 (Cauchy-Riemann Equations)

Cauchy-Riemann equations

Keywords :

it also brings out the `geometric' meaning of C-R equations. A must read for students who like geometry.
MTTS Level :
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(Downloaded 1472 times last on 25 April 2025, 10:07 pm
31
Complex Analysis: Handout-7 (Path Integrals)

Path integrals

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1044 times last on 25 April 2025, 10:07 pm
32
Complex Analysis: Handout-7 (Properties of Holomorphic Functions

Properties of holomorphic functions. No proofs.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1107 times last on 25 April 2025, 10:07 pm
33
Complex Analysis: Handout-8 (Weierstrass Theorem)

Weierstrass theorem on uniform convergence (on compact subsets) of holomorphic functions.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1154 times last on 25 April 2025, 10:07 pm
34
Connected and Path-connected Spaces

A quick introduction to connected and path-connected spaces. More details may be found in my book on metric spaces.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 4749 times last on 26 April 2025, 11:43 am
35
Construction of real numbers

Construction of real numbers

Keywords :

B.Sc./M.Sc
MTTS Level :
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(Downloaded 1228 times last on 25 April 2025, 10:07 pm
36
Banach Contraction Principle

Proofs of Banach's contraction mapping theorem and its applications to ODE and integral equations.

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 875 times last on 25 April 2025, 10:07 pm
37
Correspondence Theorem for Groups

Proves the stated result with a nontrivial application (which is missing in standard textbooks).

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1523 times last on 25 April 2025, 10:07 pm
38
Covering Spaces

Basic notions of covering spaces with emphasis on topological manifolds.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 798 times last on 25 April 2025, 11:24 pm
39
Existence of Continuous Logarithms

Proves the existence of continuous logarithms on star-shaped domains in $R^n$ with values in $C^*$. As an application, gives a proof of no-retraction theorem.

Keywords :

M.Sc.
MTTS Level :
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(Downloaded 765 times last on 25 April 2025, 10:07 pm
40
A Continuous but Nowhere Differentiable Function

Establishes the existence of a continuous nowhere differentiable function in a seriesof graded exercises. Rest assured it is easy!

Keywords :

Final year B.Sc, M.Sc
MTTS Level :
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(Downloaded 1206 times last on 25 April 2025, 10:07 pm