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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5

Question about minimum function and limit definition (proper)

  • Amad27
  • · Replies 5 ·
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5

Undergrad Prove Complex Numbers Triangle Inequality: lz-wl>=llzl-lwll

  • Unusualskill
  • · Replies 1 ·
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1

Graduate How to derive the branch cuts for complex arcsin(z)

  • monmon_4
  • · Replies 1 ·
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1

Graduate Staying Awake & Interested in Math Analysis Class

  • crownedbishop
  • · Replies 1 ·
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1

Graduate Rademacher's Theorem: Introduction to Lipschitz Continuity

  • jamilmalik
  • · Replies 1 ·
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1
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Graduate Homology Functor, Prod. Spaces, Chain Groups: Refs Needed

  • WWGD
  • · Replies 3 ·
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3

Graduate Measurability and integration of set-valued maps

  • moh salem
  • · Replies 6 ·
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6

Plotting Complex Functions: Does it Look Like a Riemann Surface?

  • Dustinsfl
  • · Replies 1 ·
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Graduate Does e^z - z^2 = 0 Have Infinite Solutions?

  • Likemath2014
  • · Replies 3 ·
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Graduate Understanding the Formula for q in Rudin's Proof Question

  • Diffy
  • · Replies 1 ·
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Graduate Complex Integral Trigonometric Substitution

  • KleZMeR
  • · Replies 3 ·
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3

Graduate How Can Set-Valued Maps Be Integrated in Measurable Spaces?

  • moh salem
  • · Replies 2 ·
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2

Is the Function f(z) = z^(1/3) Analytic?

  • Dustinsfl
  • · Replies 11 ·
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11

Defining Branch Cuts for f(z) = z^(1/3)

  • Dustinsfl
  • · Replies 9 ·
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9
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Could you explain me the definition?

  • evinda
  • · Replies 1 ·
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Graduate Spectrum of ##(x_1,x_2,x_3, )\mapsto(0,x_1,2^{-1}x_2, )##

  • DavideGenoa
  • · Replies 11 ·
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11

Graduate Proof that [0,1] is compact (not using Heine Borel). Proof check

  • fleazo
  • · Replies 2 ·
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2

Graduate Are there any metric spaces with no Cauchy sequences?

  • dumb_curiosity
  • · Replies 1 ·
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1

Proof of Outer Lebesgue Measure Monotonicity and Subadditivity

  • mathmari
  • · Replies 2 ·
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2

Graduate Can a Sphere Be Creased in UIUC's Optiverse Exploration?

  • HeavyMetal
  • · Replies 2 ·
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2

Graduate Complex Analysis: Cauchy Riemann Equations 2

  • Darth Frodo
  • · Replies 2 ·
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Graduate Complex form of Fourier series

  • etf
  • · Replies 1 ·
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What is the maximum value of f(z) for any complex number z?

  • juantheron
  • · Replies 2 ·
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Graduate Consequences of a Codimension One and One-Dimensional Foliations on Topology

  • center o bass
  • · Replies 4 ·
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4

Graduate Can a discontinuous function have a uniformly convergent Fourier series?

  • etf
  • · Replies 5 ·
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5

Graduate Interpretation of induction in terms of symmetry transformations

  • Boorglar
  • · Replies 4 ·
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4

Graduate Can All Banach Spaces Be Structured as Unitary Banach Algebras?

  • DavideGenoa
  • · Replies 14 ·
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14

Graduate Euclidean metric and non-Cartesian systems

  • rkaminski
  • · Replies 2 ·
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2

Graduate Why couldn't monotonicity be used again in examples 2 and 4 of real analysis?

  • nateHI
  • · Replies 2 ·
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2

Newbie here with question on Complex components

  • THAGONZ
  • · Replies 4 ·
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4

Graduate Integral on Circle: Showing $\frac{1}{1-|z|^2}$

  • Likemath2014
  • · Replies 2 ·
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2

Graduate On derivatives of higher order

  • jwqwerty
  • · Replies 5 ·
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5

Graduate How to think about complex integration

  • bobby2k
  • · Replies 1 ·
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1

Graduate How Does the Mobius Strip Relate to Four-Dimensional Space?

  • volcanolam
  • · Replies 7 ·
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7

Graduate 2D-Spheres with Complex Structure

  • WWGD
  • · Replies 4 ·
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4

Finding the Conjugate Function of u for f to be Analytic

  • Dustinsfl
  • · Replies 2 ·
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2

Deduce analyticity of each function

  • Dustinsfl
  • · Replies 1 ·
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1

Undergrad Understanding the Comparison of Complex and Real Numbers

  • Septimra
  • · Replies 10 ·
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10

Graduate Why is the derivative of |x| not equal to sgn(x) + 2xδ(x)?

  • IniquiTrance
  • · Replies 3 ·
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Graduate Banach Sub-Algebra of C*-Algebra: Proving Completeness

  • Fredrik
  • · Replies 5 ·
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5

Is the Set of Differentiable Points of a Function a Borel Set?

  • Fermat1
  • · Replies 3 ·
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3

Undergrad Is There a Root for cos(x) = x in the Interval (0,1)?

  • happysmiles36
  • · Replies 3 ·
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3

Cardinality of an interval as a limit

  • Fermat1
  • · Replies 3 ·
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3

Graduate Homemorphism of two metric space

  • xiavatar
  • · Replies 1 ·
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1

Graduate Help finding the equation of a line to a moving point

  • AtlasSniperma
  • · Replies 2 ·
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2

Branch Points & Cuts: Definitions & Examples

  • Dustinsfl
  • · Replies 1 ·
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Graduate Compact operator in reflexive space compact

  • DavideGenoa
  • · Replies 2 ·
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Graduate Pointwise convergence of Riemann integrable functions

  • bobby2k
  • · Replies 7 ·
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Solving Problem w/ Norm Space Proof: Advice & Resources

  • SamJohannes
  • · Replies 6 ·
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6

Graduate Is There a Connection Between Inequality and the Unit Disc?

  • Likemath2014
  • · Replies 20 ·
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20

High School Is tan(x) continuous when x = pi/2?

  • johann1301
  • · Replies 16 ·
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Proving an Inequality Involving Real Numbers

  • Julio1
  • · Replies 3 ·
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Graduate Existence of surjective linear operator

  • DavideGenoa
  • · Replies 4 ·
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Graduate Remind me how to do this complex integral

  • catsarebad
  • · Replies 8 ·
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8

Graduate Analyzing Analytic Functions: Solving a Complex Analysis Conundrum

  • Jorriss
  • · Replies 5 ·
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5

Graduate Why Does (e^(1+i*2*pi))^(1+i*2*pi) Not Equal e^((1+i*2*pi)(1+i*2*pi))?

  • eltodesukane
  • · Replies 3 ·
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3

Graduate Banach's inverse operator theorem

  • DavideGenoa
  • · Replies 10 ·
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10

Graduate Rotations in the complex plane

  • DiracPool
  • · Replies 2 ·
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2

Graduate On limit of function and proof of chain rule

  • jwqwerty
  • · Replies 3 ·
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3
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5

Graduate On differentiability on endpoints of an open interval

  • jwqwerty
  • · Replies 8 ·
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8

Graduate Are there complex functions with finite, nonzero branch points?

  • fuserofworlds
  • · Replies 4 ·
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4

Graduate Visualizing the Poincare Disc: Understanding its Limits

  • shounakbhatta
  • · Replies 4 ·
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4

Graduate A separation theorem in locally convex spaces

  • DavideGenoa
  • · Replies 11 ·
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11

Graduate Continuous functional s.t. $f(x_0)\ne 0$

  • DavideGenoa
  • · Replies 4 ·
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4

Undergrad Why study different kinds of functions in Real and Complex Analysis?

  • Sigma057
  • · Replies 5 ·
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5

What Does the Integral Expression $\int_{\gamma} \rho(z) |dz|$ Represent?

  • poissonspot
  • · Replies 1 ·
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1

Graduate Proof of Baby Rudin: Unique Real y for x & n

  • Mogarrr
  • · Replies 4 ·
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4

Yes, your solution is correct. Good job!

  • aruwin
  • · Replies 2 ·
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2

Graduate What is Dimension Theory and Its Infinite Dimensions?

  • Master Sashin
  • · Replies 23 ·
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23

Undergrad Determine function from the graph

  • Goodver
  • · Replies 1 ·
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1

Undergrad Is this an infinite number of discontinuities?

  • Hertz
  • · Replies 11 ·
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11

Graduate Beginning Group Theory, wondering if subset of nat numbers are groups?

  • mathacka
  • · Replies 2 ·
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2

Is A_epsilon Non-Empty and Measurable in Lebesgue's Theory?

  • fsblajinha
  • · Replies 3 ·
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3

Graduate Can You Solve f(x) + g(x,y) = 0 Where g Is Tangent to f?

  • ekkilop
  • · Replies 2 ·
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2

Graduate Problem in the paper of van Zwet

  • victoriaabc
  • · Replies 2 ·
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2

Undergrad How does a collection of points have dimensions?

  • elementbrdr
  • · Replies 7 ·
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7

Graduate Regions; "Each point of the set is the center of a circle "

  • Nathanael
  • · Replies 5 ·
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5

Why are the cubic roots of 1 expressed as cis 120 degrees?

  • Yankel
  • · Replies 4 ·
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4

Help with finding the sup and inf

  • Saitama
  • · Replies 2 ·
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2

Convolution of two discrete sequence

  • nacho-man
  • · Replies 1 ·
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1

Undergrad Understanding Complex Number Fundamentals

  • DiracPool
  • · Replies 17 ·
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17

Graduate Can a Matrix-Valued Function h Exist with Given Properties in GL^+(n,R)?

  • WWGD
  • · Replies 4 ·
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4

Graduate So-called Fundamental Theorem of Algebra

  • thelema418
  • · Replies 1 ·
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1

Graduate Are the Results of Adding and Subtracting ζ(0) and Grandi's Series Valid?

  • Kekasi
  • · Replies 1 ·
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1

Graduate Schwartz - Christoffel transformation: point at infinity confusion

  • D_Tr
  • · Replies 2 ·
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2

Graduate Is there a table of Abel transforms for Gaussian distributions available?

  • Mr Boom
  • · Replies 1 ·
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1

Graduate Orthogonality and physical applications

  • 16universes
  • · Replies 17 ·
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17

Graduate Proof of rational density using Dedekind cuts

  • loops496
  • · Replies 5 ·
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5

Graduate Exponentiation with zero base, complex exponent?

  • bcrowell
  • · Replies 9 ·
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9

Graduate Computing Čech cohomology groups

  • Geometry_dude
  • · Replies 2 ·
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2

Graduate Are complex numbers just means to an end?

  • jaydnul
  • · Replies 21 ·
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21

Graduate Understanding Big O Notation: Limit Definition and Reconciling Statements

  • ericm1234
  • · Replies 7 ·
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7

Graduate Separating hyperplane theorem for non-disjoint sets

  • economicsnerd
  • · Replies 2 ·
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2

Undergrad Metrics on the plane and the sphere

  • gianeshwar
  • · Replies 6 ·
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6

Undergrad What are some open problems that would make a good honors thesis.

  • Silvers931
  • · Replies 5 ·
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