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

Upper-Lower sum of Riemann Integral

  • evinda
  • · Replies 3 ·
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3

Are Measures Really Equal If Integrals of Continuous Functions Match?

  • Gerald1
  • · Replies 3 ·
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3

Graduate Limits of "Proper" Function Approach to Banach Spaces

  • BDV
  • · Replies 4 ·
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4

What is the value of z if its argument is equal to its conjugate?

  • Saitama
  • · Replies 23 ·
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23

Examples of spectral decompositions

  • Boromir
  • · Replies 3 ·
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3

Graduate Kantorovich Norm Explained: Pushforward Measure & Integration

  • johnqwertyful
  • · Replies 2 ·
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2

Can Complex Integration Solve These Advanced Calculus Problems?

  • youth4ever
  • · Replies 8 ·
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8

Undergrad Complex conjugate of a complicated function

  • BomboshMan
  • · Replies 1 ·
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1

Calculating Fourier Cosine Series of cos(x) from 0 to \pi

  • Suvadip
  • · Replies 4 ·
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4

Proving x^8+1=P_0^3(x^2-2xcos(2k+1)π/8+1)

  • Suvadip
  • · Replies 2 ·
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2

Undergrad Some remarks on complex numbers

  • ClamShell
  • · Replies 66 ·
3
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66

Graduate Fourier transform and the frequency domain

  • Bipolarity
  • · Replies 6 ·
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6

There are a,b>=0, such that |f(x)|<= ax+b

  • evinda
  • · Replies 10 ·
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10

Second mean value theorem in Bonnet's form

  • Suvadip
  • · Replies 1 ·
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1

Is $f(x)=\sqrt{x},x\geq 0$ Lipschitz at $[0,\infty]$?

  • evinda
  • · Replies 18 ·
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18

Show that gof is uniformly continuous

  • evinda
  • · Replies 4 ·
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4

Differentiability of complex function

  • Suvadip
  • · Replies 2 ·
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2

Prove Real Roots of $x^3+ax+b=0$ When $a<0$

  • anemone
  • · Replies 4 ·
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4

Graduate Would anyone like to comment on my proof?

  • Jyan
  • · Replies 8 ·
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8
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6

If an operator commutes, its inverse commutes

  • Boromir
  • · Replies 1 ·
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1

Undergrad How exp(jwt)=cos(wt)+jsin(wt)?

  • nomisme
  • · Replies 4 ·
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4

Limit superior and limit inferior

  • Suvadip
  • · Replies 1 ·
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1

Proving Continuity in a Rectangle Using f(x,y) Function

  • Suvadip
  • · Replies 1 ·
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1

Munkres' 'Analysis on Manifolds' Question.

  • caffeinemachine
  • · Replies 4 ·
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4

Undergrad In the complex number system, why can't 1+1 = 0 ?

  • pondzo
  • · Replies 25 ·
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25

Continuous extension of homomorphism

  • Boromir
  • · Replies 7 ·
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7

Graduate Is there any intro topics involving topology and physics?

  • ozone
  • · Replies 5 ·
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5
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6

Graduate Give me example of antipodal set in infinite dimensional?

  • parisa
  • · Replies 1 ·
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1

Showing a certain algebra is closed under inverses

  • Boromir
  • · Replies 9 ·
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9

Graduate Why Doesn't the Fourier Series of a Dirac Comb Match Pointwise Values?

  • sahil_time
  • · Replies 7 ·
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7

Show that there is a z such that f(z)=0

  • evinda
  • · Replies 5 ·
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5

Show that if Σ((an)/(1+an)) converges,then Σan also converges

  • evinda
  • · Replies 4 ·
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4

Are Simple Functions Dense in Bounded Borel Functions on a Compact Space?

  • Fermat1
  • · Replies 3 ·
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3

How is this inequality obtained?

  • Boromir
  • · Replies 5 ·
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5

Undergrad 2 definitions for argument, why?

  • Jhenrique
  • · Replies 3 ·
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3

How Can Complex Analysis Be Used to Sum Powers of Sine Functions?

  • Suvadip
  • · Replies 1 ·
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1

Proving Homomorphism in Commutative Subalgebras of Bounded Operators

  • Boromir
  • · Replies 9 ·
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9

Undergrad Contradiction in the definition and properties of the abs

  • Jhenrique
  • · Replies 2 ·
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2

Graduate Is the space of tempered distributions 1st countable ?

  • dextercioby
  • · Replies 6 ·
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6

Graduate Real numbers without set theory

  • Fredrik
  • · Replies 6 ·
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6

Graduate Topological indistinquisable points and set theory.

  • center o bass
  • · Replies 18 ·
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18

Finding Minimum Value of Polynomial Function f

  • evinda
  • · Replies 8 ·
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8

Graduate Question on Definition of Cover of a Set

  • BrainHurts
  • · Replies 3 ·
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3

Undergrad Hyperbolic Sine - Exponent transition

  • porcupineman23
  • · Replies 2 ·
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2

Show that the limit is equal to zero

  • mathmari
  • · Replies 5 ·
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5

Graduate Surface height from surface normal function

  • AndrewD
  • · Replies 1 ·
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1

Show that two subsequences are monotonic and bounded

  • evinda
  • · Replies 10 ·
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10

Does the Sequence Diverge Using Inequalities?

  • evinda
  • · Replies 4 ·
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4

Is f(x) Differentiable at x=0?

  • evinda
  • · Replies 4 ·
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4

Show that there is a M>0 such that |f(x)|<M

  • mathmari
  • · Replies 11 ·
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11

Can the sequence be determined by finding the difference?

  • evinda
  • · Replies 5 ·
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5

Undergrad Can Complex Numbers in Polar Format Be Equated Like Real Numbers?

  • KrayzBlu
  • · Replies 3 ·
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3

Graduate Dyadic Squares in the Unit Disc: A Proof and Critique

  • Someone2841
  • · Replies 1 ·
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1

Graduate How to interpret this problem involving dyadic squares and unit disc?

  • Someone2841
  • · Replies 1 ·
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1

Graduate Understanding the Open Set: Definition & Examples

  • hideelo
  • · Replies 19 ·
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19
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14

Graduate How would one prove that algebraic topology can never have a non self-

  • Amsingh123
  • · Replies 8 ·
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8

Graduate Can We Visualize the Fifth Dimension?

  • Bluskyz
  • · Replies 2 ·
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2

Graduate Interpreting Complex Solutions in Cubic Bezier Curve Problems

  • treddie
  • · Replies 4 ·
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4

Question about decreasing sequence and finding its limit

  • evinda
  • · Replies 7 ·
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7

Fixed Point Theorem: Estimating x* With x9 & x10

  • evinda
  • · Replies 2 ·
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2

Graduate Can open sets and closures intersect in a topological space?

  • Shaji D R
  • · Replies 8 ·
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8

Graduate Approximating function by trigonometric polynomial

  • ekkilop
  • · Replies 3 ·
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3

Graduate Projection to Invariant Functions:

  • l'Hôpital
  • · Replies 3 ·
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3

Graduate Möbius Transformations <=> holomorphic and 1-to-1?

  • nonequilibrium
  • · Replies 1 ·
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1

Can a Continuous Curve Only Intersect a Differentiable Curve at the Origin?

  • caffeinemachine
  • · Replies 3 ·
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3

Graduate How to derive beta function as pochhammer contour integral?

  • jackmell
  • · Replies 12 ·
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12

What are the possible values of $x+y$ in this complex number problem?

  • Saitama
  • · Replies 8 ·
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8

Graduate If all elements of a set are individually bounded, is the set bounded?

  • leinadle
  • · Replies 5 ·
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5

The sine inverse of a purely complex number

  • Suvadip
  • · Replies 5 ·
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5

Pointwise convergence implies uniform convergence

  • Siron
  • · Replies 1 ·
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1

Parameterization for a Straight Line

  • nacho-man
  • · Replies 3 ·
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3
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5

Graduate Complex Made Simple: Notation on Disks

  • BrainHurts
  • · Replies 3 ·
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3

Graduate How to check if function is differentiable at a point

  • Fabio010
  • · Replies 1 ·
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1

Graduate Norms of compositions of bounded operators between different spaces

  • AxiomOfChoice
  • · Replies 2 ·
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2

Graduate Finding Derivatives of Analytic Functions: Chain Rule Confusion

  • Natura
  • · Replies 6 ·
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6

How do I solve complex number z^4+16=0

  • Raerin
  • · Replies 23 ·
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23

Complex Number Equation: Why Does a+bi=1 Not Give the Final Answer?

  • Raerin
  • · Replies 6 ·
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6

Graduate Heegard Splitting of the 2-Torus.

  • WWGD
  • · Replies 2 ·
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2

Graduate Homotopy and Continuous Functions

  • WWGD
  • · Replies 24 ·
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24

Graduate Principles Of Mathematical Analysis-Walter Rudin

  • Shaji D R
  • · Replies 10 ·
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10

Graduate Definition of a circle in point set topology.

  • center o bass
  • · Replies 38 ·
2
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38

Undergrad Is Sqrt(-1) not unique? I.e. is i not the only one?

  • Curl
  • · Replies 4 ·
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4

Does Euclid's Fifth Postulate Apply to Non-Flat Surfaces Like Spheres?

  • JamieLam
  • · Replies 4 ·
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4

Graduate Consecutive Reals: A Hypothetical Possibility?

  • hddd123456789
  • · Replies 39 ·
2
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39

Graduate Need help with simple proof, metric space, open covering.

  • bobby2k
  • · Replies 7 ·
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7

Two questions, one on harmonic functions

  • nacho-man
  • · Replies 3 ·
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3

Proving Absolute Convergence of a Real-Valued Function on a Sigma Algebra

  • Fermat1
  • · Replies 1 ·
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1

Graduate Continuity of the inverse of a linear operator

  • AxiomOfChoice
  • · Replies 2 ·
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2

Graduate Inequality integral absolute value derivative

  • jostpuur
  • · Replies 12 ·
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12

Pointwise Conv. | Does $f_{n}$-$f$ -> 0 for Each x?

  • Fermat1
  • · Replies 2 ·
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2

Graduate Convex sets - How do we get (1−t)x+ty

  • bhagwad
  • · Replies 3 ·
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3

Graduate Idea behind topological manifold definition.

  • center o bass
  • · Replies 3 ·
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3
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8

Graduate Establishing that a function is discontinous

  • center o bass
  • · Replies 2 ·
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2

Graduate Inverse Function Thm. and Covering Maps.

  • WWGD
  • · Replies 2 ·
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2

Graduate Principles Of Mathematical Analysis-Walter Rudin

  • Shaji D R
  • · Replies 1 ·
Replies
1