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

Is the Absolute Convergence Theorem Sufficient to Prove This?

  • alexmahone
  • · Replies 1 ·
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1

Graduate Weakly sequentially compact supsets

  • rlukach
  • · Replies 2 ·
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2

Graduate Is an Open Interval Homeomorphic to R?

  • fleazo
  • · Replies 7 ·
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7

Undergrad Complex conjugate of absolute exponential

  • vg8open
  • · Replies 7 ·
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7

Struggling with Fourier Transform Eigenvalues?

  • Stephen88
  • · Replies 3 ·
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3

Complex integral oriented counterclockwise

  • Dustinsfl
  • · Replies 5 ·
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5

Evaluating Complex Integration I_c |z^2|

  • AkilMAI
  • · Replies 6 ·
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6

Power Series Expansion: Solving for 1/1+z at z=-5 with Radius of Convergence

  • Stephen88
  • · Replies 11 ·
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11

Show that C.R conditions are held.

  • Also sprach Zarathustra
  • · Replies 4 ·
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4

Proof of Cauchy Sequence for $\{a_n\}$ Defined by $f(x)$

  • alexmahone
  • · Replies 6 ·
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6

Proofs of Supremum Problem in $\mathbb{R}$

  • alexmahone
  • · Replies 10 ·
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10

Another supremum and infimum problem

  • alexmahone
  • · Replies 5 ·
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5

How Does Scaling a Set Affect Its Supremum and Infimum?

  • alexmahone
  • · Replies 2 ·
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2

Proof of $A\subseteq B\implies\sup A\le\sup B$

  • alexmahone
  • · Replies 2 ·
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2

How Does Complex Analysis Explain Geometry and Entire Functions?

  • Markov2
  • · Replies 8 ·
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8

Graduate One-point compactification of space of matrices with positive trace

  • julian
  • · Replies 6 ·
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6

When does a complex function have a simple zero on a given interval?

  • Markov2
  • · Replies 10 ·
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10
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14

Understanding Complex Functions and Polynomials in the Complex Plane

  • Markov2
  • · Replies 6 ·
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6

Solving $\sin(z) = 2 + 3i$ using complex numbers

  • Dustinsfl
  • · Replies 17 ·
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17

Analytic on D: Power Series and Polynomial Coefficients

  • Dustinsfl
  • · Replies 6 ·
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6

Find principal value in a+ib form.

  • paulbk108
  • · Replies 6 ·
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6

Prove $\inf \{\overline{m}-x: x\in S\}=0$

  • alexmahone
  • · Replies 3 ·
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3

Can Analytic Functions Exhibit These Complex Behaviors?

  • Markov2
  • · Replies 9 ·
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9

Graduate What does the frequency representation of a function show?

  • Tosh5457
  • · Replies 5 ·
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5

How Do Complex Numbers Relate to the Unit Disk and Their Properties?

  • Markov2
  • · Replies 5 ·
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5

Graduate Is the Pre-Image Always Open in Topological Spaces?

  • Jooolz
  • · Replies 6 ·
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6

Bounded Function on Set S: Proving $|f(z)|\le1$ for All $z\in S$

  • Markov2
  • · Replies 10 ·
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10
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6

How Can I Create a Mobius Transformation?

  • Stephen88
  • · Replies 3 ·
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3
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6

Proving Nested Intervals Converge to $\alpha$

  • alexmahone
  • · Replies 2 ·
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2

Graduate Co-finite topology on an infinite set

  • Deveno
  • · Replies 2 ·
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2

Uniform Convergence of $Y(x)$ in $(0,1]$

  • Also sprach Zarathustra
  • · Replies 5 ·
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5

Expanding f(z) with Powers of z-1

  • Dustinsfl
  • · Replies 13 ·
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13

Graduate Equivalent definition of the supremum

  • submartingale
  • · Replies 5 ·
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5

How to prove $a_n\to 0$ using the sequence location theorem?

  • alexmahone
  • · Replies 4 ·
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4

Can Complex Equations Be Solved More Efficiently?

  • Markov2
  • · Replies 9 ·
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9

How do I expand $f(z)$ into a power series?

  • Dustinsfl
  • · Replies 12 ·
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12

Complex Integral: Solving a Difficult Problem

  • Advent
  • · Replies 8 ·
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8

Does Convergence of a Sequence Imply Convergence of Its Absolute Values?

  • alexmahone
  • · Replies 5 ·
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5

What Values of z Make This Series Converge?

  • Dustinsfl
  • · Replies 9 ·
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9

Holomorphic function and an open disc

  • Stephen88
  • · Replies 3 ·
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3

Graduate Notation for set of limit points?

  • nonequilibrium
  • · Replies 2 ·
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2

Does an Increasing Sequence Bounded by a Convergent Sequence Converge?

  • alexmahone
  • · Replies 2 ·
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2

Graduate What does it mean for a space to be naturally identified with another?

  • daveyp225
  • · Replies 7 ·
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7

Graduate Is a convex subset of a connected space connected?

  • nonequilibrium
  • · Replies 2 ·
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2

Prove that there is a strictly decreasing sequence

  • alexmahone
  • · Replies 2 ·
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2

Solving Fourrier Transform Problems: Schwartz Space & exp(-ax^2)

  • AkilMAI
  • · Replies 6 ·
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6

T - Improving Upper Bound for $a_n$ in Series for $n$

  • alexmahone
  • · Replies 6 ·
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6

Graduate What Does the Product of Spheres Look Like?

  • Jooolz
  • · Replies 13 ·
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13

Prove that the sequence converges to 0 (2)

  • alexmahone
  • · Replies 2 ·
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2

Prove that the sequence converges to 0

  • alexmahone
  • · Replies 3 ·
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3

Graduate A metric space of equivalent sequence classes

  • goedelite
  • · Replies 11 ·
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11

High School Complex Conjugate: just replace i by -i even in denominator or inside argument?

  • aimforclarity
  • · Replies 12 ·
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12

Graduate Completeness of ℝ (when ℝ is defined abstractly)

  • Fredrik
  • · Replies 2 ·
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2

Graduate Metric function composed with concave function

  • shoescreen
  • · Replies 5 ·
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5

Graduate Is the Empty Set Axiom Redundant in Ultrafilters?

  • alexfloo
  • · Replies 6 ·
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6

Graduate How the value of ln(-1) is derived

  • Benn
  • · Replies 1 ·
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1

Graduate Looking for a metric to express difference between two curves

  • meldraft
  • · Replies 6 ·
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6

Undergrad Anyone here ever got bugged with i?

  • fbs7
  • · Replies 61 ·
3
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61

Graduate Example in topology: quotient maps and arcwise connected

  • nonequilibrium
  • · Replies 3 ·
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3

Graduate Graphing a function in a Normed linear space

  • bugatti79
  • · Replies 2 ·
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2

Graduate Counterexample intersections of 2 compacts is compact ?

  • nonequilibrium
  • · Replies 7 ·
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7

Graduate Weak convergence of orthonormal sequences in Hilbert space

  • kisengue
  • · Replies 3 ·
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3

Graduate Why category in Baire's Category Theorem?

  • goedelite
  • · Replies 4 ·
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4

Undergrad Splitting an exponential complex number into real and imaginary parts

  • dan5
  • · Replies 2 ·
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2

Graduate Sketching exponential curves with complex numbers

  • dan5
  • · Replies 4 ·
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4

Graduate What are the biggest questions in topology and abstract algebra?

  • kramer733
  • · Replies 4 ·
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4

Graduate Every uncountable subset of R has a limit point in Q?

  • nonequilibrium
  • · Replies 4 ·
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4

Graduate [topology] new kind of separation axiom? where does it fit in?

  • nonequilibrium
  • · Replies 2 ·
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2

Graduate Help me, nearest neighbor problem.

  • phaothu365
  • · Replies 2 ·
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2

Undergrad Taking a number to a complex number power

  • ucbugrad
  • · Replies 3 ·
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3

Undergrad What Does It Mean for a Function to Be Single Valued?

  • Hermes10
  • · Replies 4 ·
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4

Graduate A question about subspace topolgy

  • ShahidNawaz
  • · Replies 6 ·
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6

Graduate Interior Product: Find from Exterior Product

  • joebohr
  • · Replies 10 ·
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10

Graduate A Question about Topological Connectivity

  • RVM45
  • · Replies 2 ·
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2

Graduate Are Convergence Sequences Unique in a Normed Linear Space?

  • bugatti79
  • · Replies 18 ·
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18

Graduate Verify: Topology of Point-Set Question Needs to be First Countable

  • Poopsilon
  • · Replies 2 ·
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2

Graduate A problem about equivalent metric

  • prophetlmn
  • · Replies 3 ·
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3

Graduate Boundary points of subsets when viewed with the subset topology

  • Damidami
  • · Replies 4 ·
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4

Graduate Connecting homomorphism question

  • panzervlad
  • · Replies 2 ·
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2

Graduate Help with continuous functions in metric spaces

  • h20o85
  • · Replies 4 ·
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4

Undergrad Why does the graph of y = ln(x) have an imaginary part?

  • rollcast
  • · Replies 4 ·
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4

Graduate Is there an interesting way to define a continuous composition of functions?

  • Stephen Tashi
  • · Replies 4 ·
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4

Graduate Distance between sets (a triangle-type inequality)

  • Identity
  • · Replies 2 ·
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2

Graduate Compactness is topology-independent ?

  • dextercioby
  • · Replies 7 ·
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7

Graduate Group of translations on real line with discrete topology

  • xboy
  • · Replies 3 ·
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3

Graduate S^2 union a line connecting the north and south pole

  • mathsq
  • · Replies 6 ·
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6

Graduate How Can I Better Understand Metric Space Problems?

  • Someguy25
  • · Replies 2 ·
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2

Undergrad What Determines the Angle of a Complex Number in Polar Form?

  • carlodelmundo
  • · Replies 2 ·
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2

Graduate Is {X, max(d,r)} or (X, min(d,r)) a Metric Space?

  • ag2ie
  • · Replies 8 ·
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8

Graduate Applied Functional Analysis by Zeidler

  • _DJ_british_?
  • · Replies 2 ·
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2

Undergrad Is the complex plane meaningful?

  • 1MileCrash
  • · Replies 4 ·
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4

Graduate What Should an Engineer Know Before Studying Topology?

  • boneh3ad
  • · Replies 20 ·
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20

Undergrad Help proving complex inequality

  • JerryG
  • · Replies 1 ·
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1

Graduate How to prove that SU(3) is compact

  • zahero_2007
  • · Replies 25 ·
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25

Graduate Compactness of (0,1) when that is the whole metric space

  • deckoff9
  • · Replies 7 ·
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7

Graduate Defining an Empty Set Metric Space: Understanding Properties of d

  • zooxanthellae
  • · Replies 7 ·
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7

Graduate Does Convergence of (sn) and (sntn) Imply (tn) Converges?

  • gsmith89
  • · Replies 2 ·
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2