Topology and Analysis Forum

Participate in expert discussion on topology and analysis topics. This includes point-set topology, Real, complex, harmonic and functional analysis. Also measure and integration theory.

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Threads

Prove $f(x)=Cx$ for All $x$: Functional Equation

  • alexmahone
  • · Replies 5 ·
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5

Graduate Are Complex Primes a Reality or Just a Concept?

  • Dashin
  • · Replies 9 ·
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9

Graduate Can a Complex Plane Applet Graph xx = i?

  • Frogeyedpeas
  • · Replies 1 ·
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1

Graduate Definition of Limit Point: Is There a Point Not in E?

  • jwqwerty
  • · Replies 5 ·
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5

Help with Hyperbolic Functions

  • CaptainBlack
  • · Replies 1 ·
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1

Trig integration complex analysis

  • Dustinsfl
  • · Replies 4 ·
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4

Integration--Cauchy Principal Value, Residue, line integration, poles

  • Dustinsfl
  • · Replies 5 ·
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5

Give an example of a convergent series

  • alexmahone
  • · Replies 2 ·
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2

Subsequence - absolute convergence

  • alexmahone
  • · Replies 2 ·
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2

Graduate General question regarding continuous functions and spaces

  • TwilightTulip
  • · Replies 1 ·
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1

How Does Complex Analysis Explain the Integral of Sin^2(x)/x^2?

  • Dustinsfl
  • · Replies 9 ·
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9

Graduate Invariance of Domain: Showing U Open in Differential Geometry | Spivak Ch.1

  • Rasalhague
  • · Replies 4 ·
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4

Show a certain sequence in Q, with p-adict metric is cauchy

  • arturo_026
  • · Replies 1 ·
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1

Graduate What kind of math notation is this?

  • muffinman123
  • · Replies 3 ·
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3

Improper complex integrals--residue

  • Dustinsfl
  • · Replies 2 ·
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2

Graduate Is my understanding of open sets and bases in topology correct?

  • Question Man
  • · Replies 2 ·
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2
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2

Circle radius 2 oriented counterclockwise

  • Dustinsfl
  • · Replies 2 ·
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2

Number of Zeros Inside Unit Circle for Polynomial P(z)

  • Dustinsfl
  • · Replies 7 ·
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7

Graduate Proving the Validity of a New Metric Space

  • Lily@pie
  • · Replies 8 ·
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8

Proving Convergence of e^z Series Using Ratio Test on Coefficients

  • Poirot1
  • · Replies 6 ·
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6

Solving $z^4=-1$ with a Complex Number

  • Dustinsfl
  • · Replies 5 ·
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5

Analyzing the Complex Function $g(z)$

  • Dustinsfl
  • · Replies 3 ·
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3

How is the Steepest Descent Formula Used to Solve Linear Systems?

  • Amer
  • · Replies 1 ·
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1

Complex Numbers III: Solving z^5-(z-i)^5=0

  • Punch
  • · Replies 3 ·
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3

Graduate Help me parse the logic of this statement

  • Poopsilon
  • · Replies 2 ·
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2

Inf{frac{n*sqrt(3)} : n in integer}=0

  • caffeinemachine
  • · Replies 11 ·
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11

Graduate Whats an infinite intersection of open sets

  • natasha d
  • · Replies 8 ·
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8

What is the Integral of a Function Around a Rectangle Oriented Clockwise?

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate What Is the Boundary of a Product Manifold?

  • mma
  • · Replies 9 ·
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9

Convergence of Ratio Test for Complex Numbers z in C

  • Dustinsfl
  • · Replies 5 ·
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5

Quick question about continuous mapping

  • arturo_026
  • · Replies 1 ·
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1

Integrating $\tan z$ Around a Circle of Radius 8

  • Dustinsfl
  • · Replies 5 ·
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5

Graduate Cardinality of the Preimage f^{-1}(y) of f:X->Y continuous?

  • Bacle2
  • · Replies 8 ·
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8

Solve for Complex Number \(z\) Given \(4+i(4z+1)=2re^{i(\pi+\theta)}\)

  • Punch
  • · Replies 14 ·
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14

A Quick Question About Orthornomal Systems of Functions and Fourier Series

  • TaylorM0192
  • · Replies 1 ·
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1

Fourier Transform: Proving $G(z)$ is an Entire Function

  • Dustinsfl
  • · Replies 6 ·
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6

Find the Modulus & Argument of \(wz\)

  • Punch
  • · Replies 2 ·
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2

Graduate Glueing together normal topological spaces at a closed subset

  • conquest
  • · Replies 4 ·
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4

Graduate Closed set as infinite intersection of open sets

  • lonewolf5999
  • · Replies 4 ·
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4

Is My Complex Integral Calculation Correct?

  • hmmmmm
  • · Replies 2 ·
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2

Problem 9 section 3.3 from Bartle

  • issacnewton
  • · Replies 10 ·
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10

Well-Definedness and C^Infinity Closure of Convolutions

  • TaylorM0192
  • · Replies 2 ·
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2

Surjectivity of an Isometry given the metric space is complete.

  • arturo_026
  • · Replies 1 ·
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1

How Do You Calculate the Limit of M*exp(D*exp(c*t)) as t Approaches Infinity?

  • charlottewill
  • · Replies 1 ·
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1

Is f Holomorphic on D if and only if p_g = 0 on D?

  • Stephen88
  • · Replies 2 ·
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2

Residue Theorem: Find Residue at 0 for e^z/z^3

  • Dustinsfl
  • · Replies 4 ·
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4

Graduate Julia Sets: Periodic and Non-Periodic Points Explained

  • Kortirion
  • · Replies 1 ·
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1

Finding values for a harmonic function

  • Stephen88
  • · Replies 2 ·
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2

Proving No Simple Pole at 0 for $f'$ on $\mathbb{D} - \{0\}$

  • Dustinsfl
  • · Replies 7 ·
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7

A guide to Calculating the Laurent Series of $\frac{33}{(2z - 1)(z + 5)}$

  • Dustinsfl
  • · Replies 2 ·
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2
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1

Graduate From continuity to homeomorphism, compactness in domain

  • jostpuur
  • · Replies 2 ·
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2
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2

Graduate Is Boundedness Applicable to Topological Spaces?

  • blahblah8724
  • · Replies 1 ·
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1

Solve Riemann Integral: Show \( \int_a^b f = \lim U_n = \lim L_n \)

  • Fantini
  • · Replies 2 ·
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2

Undergrad Open Set Image: Is Constant Function's Image Open?

  • zendani
  • · Replies 9 ·
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9

What is Arzela's Lemma in Fichtengoltz's Book?

  • Also sprach Zarathustra
  • · Replies 1 ·
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1

Undergrad Does Sequence (n,1/n) Converge or Diverge?

  • zendani
  • · Replies 6 ·
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6

Graduate How to prove that a topological space is non-hausdorff?

  • AdrianZ
  • · Replies 5 ·
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5

Graduate Clopen Sets: Closure = Interior?

  • blahblah8724
  • · Replies 9 ·
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9

Holomorphic Function Continuity and Holomorphicity on Real Interval [2,5]

  • Dustinsfl
  • · Replies 6 ·
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6

Graduate Is a Space Connected if Its Closure Is Connected?

  • blahblah8724
  • · Replies 4 ·
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4

Understanding Normed Linear Spaces: Convergence in C[0,1]

  • bugatti79
  • · Replies 2 ·
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2

Proving Continuity of $$ \int_{-\pi}^{\pi}te^{xt}\cos(yt)g(t)dt$$

  • Dustinsfl
  • · Replies 8 ·
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8

Graduate Can the Superior Limit of a Sequence Be Lower Than Its Supremum?

  • IniquiTrance
  • · Replies 2 ·
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2

Graduate Is This a Valid Topology on [0, ∞)?

  • blahblah8724
  • · Replies 2 ·
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2

Is the Triangle Inequality Valid for Natural Numbers and Complex Numbers?

  • Dustinsfl
  • · Replies 4 ·
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4

Uniform Convergence of f{_n} in Complex Analysis on S=[0,infinity)

  • Poirot1
  • · Replies 3 ·
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3

What is Problem 167 in Serge Lang's Complex Analysis about?

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate Definition of a Topological Space

  • Jamma
  • · Replies 3 ·
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3

Is this approach to evaluating a complex integral valid?

  • polygamma
  • · Replies 1 ·
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1
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1

N th root of a positive number is positive ....

  • issacnewton
  • · Replies 4 ·
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4

What is the Limit of the Sequence Defined by \( z_{n+1}=\sqrt{a+z_n} \)?

  • issacnewton
  • · Replies 7 ·
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7

Graduate Are all open sets compact in the discrete topology?

  • Useful nucleus
  • · Replies 9 ·
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9

Complex integration no Residue Theory everything else is ok

  • Dustinsfl
  • · Replies 5 ·
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5

Analytic Functions on the Unit Disc

  • Dustinsfl
  • · Replies 7 ·
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7

How to Express Cauchy Integral Formula in Terms of a Power Series?

  • Dustinsfl
  • · Replies 10 ·
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10

Convergence Condition for Applying Ratio Test to Power Series

  • alexmahone
  • · Replies 2 ·
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2

High School Can someone help with Argand plane graphing and finding the radius?

  • AlchemistK
  • · Replies 6 ·
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6

Prove Limit of |a_n|^(1/n) = L

  • alexmahone
  • · Replies 7 ·
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7

Is the Series $\displaystyle\sum\frac{\sin n}{n}$ Absolutely Convergent?

  • alexmahone
  • · Replies 2 ·
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2

Proof of Winding Number 1 for Analytic $f$

  • Dustinsfl
  • · Replies 2 ·
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2

Is the Sequence \(X\) Convergent or Bounded?

  • issacnewton
  • · Replies 9 ·
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9

I guess it will be the same as i,1-i

  • AkilMAI
  • · Replies 2 ·
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2

Undergrad What is the difference between the phase and argument of a complex number?

  • eggshell
  • · Replies 1 ·
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1

Complex Integral: $\int_0^1$ Calculation

  • Dustinsfl
  • · Replies 17 ·
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17

Circle radius 2 complex integration

  • Dustinsfl
  • · Replies 11 ·
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11

Primitive e^z/z Gamma: Finding the Integral

  • Dustinsfl
  • · Replies 8 ·
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8

Finding the Primitive of a Complex Integral

  • Dustinsfl
  • · Replies 3 ·
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3

Graduate Is the Sum of Two Elements in a Convex Compact Subset of R^2 Also in the Subset?

  • almostsure
  • · Replies 1 ·
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1

Absolute Convergence: Proving $\sum a_n$ is Convergent

  • alexmahone
  • · Replies 5 ·
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5

SE Class 12 Maths Alternating Series Test

  • alexmahone
  • · Replies 19 ·
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19

Undergrad How to tell that 1/(z+2i) is not analytic?

  • nutcase21
  • · Replies 3 ·
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3

Does the Converse of the Ratio Test Always Hold for Convergent Series?

  • alexmahone
  • · Replies 5 ·
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5

Convergence of $\displaystyle\sum\frac{n^5}{2^n}$

  • alexmahone
  • · Replies 3 ·
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3

Solving Attached Problem, Plus MHF Update

  • Cairo
  • · Replies 11 ·
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11

When does the series $\sum_2^\infty\frac{1}{n(\ln n)^p}$ diverge for $p<0$?

  • alexmahone
  • · Replies 2 ·
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2

Does the series $\sum_1\sin\left(\frac{1}{n}\right)$ converge?

  • alexmahone
  • · Replies 2 ·
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2