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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Graduate Does the Equation (e2Pi i)i = 1 Have a Geometric Meaning?

  • abhi2005singh
  • · Replies 6 ·
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6

Graduate Can degenerate rectangles be cartesian products of singletons in R^n?

  • JG89
  • · Replies 1 ·
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1

Graduate Why is the supremum of measurable functions measurable?

  • Tedjn
  • · Replies 6 ·
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6

High School Is -i Equal to 1/i in Complex Numbers?

  • trister
  • · Replies 8 ·
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8

Undergrad Functional analysis applications

  • cfddjk
  • · Replies 3 ·
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3

Graduate Trig identity in complex multiplication

  • Shaybay92
  • · Replies 5 ·
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5

Graduate Is Re(f) and Im(f) always differentiable for complex functions?

  • nonequilibrium
  • · Replies 11 ·
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11

Graduate Cosine = Contraction? (Banach)

  • nonequilibrium
  • · Replies 5 ·
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5

Undergrad Complex numbers, solving polynomial, signs of i

  • Platypus26
  • · Replies 3 ·
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3

Graduate Smoothness of Fourier Transforms for Rapidly Decaying Functions

  • mnb96
  • · Replies 7 ·
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7

Graduate Can Ln(-x) Ever Yield a Valid Solution Similar to Complex Numbers?

  • Simon43254
  • · Replies 9 ·
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9

Graduate What are Sobolev Spaces and why do they depend on dimension?

  • muzialis
  • · Replies 8 ·
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8

Graduate Solving Complex Functions: Evaluating at z=z_0

  • Jerbearrrrrr
  • · Replies 2 ·
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2

Graduate An expression in functional analysis

  • Charles49
  • · Replies 3 ·
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3

Undergrad Identity map and Inverse Image

  • wayneckm
  • · Replies 1 ·
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1

Graduate Knot Theory and higher dimensions

  • Galap
  • · Replies 1 ·
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1

Graduate Why is 1^(1/6) equal to cis(n*pi/3)?

  • dsanz
  • · Replies 9 ·
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9

Graduate Fourier phase (unwrapping problem)

  • mnb96
  • · Replies 2 ·
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2

Undergrad What's the formula for adding two complex numbers in polar form?

  • Juwane
  • · Replies 12 ·
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12

Graduate Monotonicity of convex function

  • hellbike
  • · Replies 1 ·
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1

Graduate How to Compute Residues of cot(piz)f(z)?

  • ~Death~
  • · Replies 1 ·
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1

Graduate Non-Hausdorff spaces by John L. Bell.

  • sutupidmath
  • · Replies 4 ·
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4

Undergrad Inequalities of real and complex numbers

  • Char. Limit
  • · Replies 3 ·
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3

Graduate Definition and properties of polar sets

  • typhoonss821
  • · Replies 1 ·
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1

Graduate Can we define all reals between two integers as limits of rational numbers?

  • Gear300
  • · Replies 3 ·
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3

Undergrad Solving for |a| in a Complex Number Equation

  • aviravir1
  • · Replies 4 ·
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4

Graduate Difference between complete and sequentially compact metric spaces

  • Hymne
  • · Replies 4 ·
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4

Graduate What is an example of a non-closed subspace in a normed space?

  • quasar987
  • · Replies 7 ·
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7

High School Domain Notation: Continuous Function

  • Shaybay92
  • · Replies 8 ·
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8

Undergrad How Does the Inverse of a Complex Number Affect Its Magnitude and Argument?

  • plexus0208
  • · Replies 4 ·
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4

Graduate Why does e^x have no roots despite its infinite degree power series?

  • Mentallic
  • · Replies 5 ·
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5

Undergrad Complex Numbers: Why Use Complex Conjugate?

  • EngWiPy
  • · Replies 4 ·
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4

Undergrad Finding the square root of a+bi (complex number)

  • Georgepowell
  • · Replies 14 ·
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14

Graduate Solving e^(1/z) + 1/(1-e^(1/z)) = w for complex z

  • AxiomOfChoice
  • · Replies 2 ·
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2

Undergrad How Do You Correctly Convert Complex Numbers to Mod-Arg Form?

  • Mentallic
  • · Replies 3 ·
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3

Graduate Basic question: meaning of partition of R into maximal connected intervals

  • seeker101
  • · Replies 1 ·
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1

Graduate Subspace/induced/relative Topology Definition

  • filter54321
  • · Replies 3 ·
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3

Undergrad Division with the rectangular form

  • Truthlover
  • · Replies 4 ·
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4

Graduate Graphing functions of two complex variables.

  • pbandjay
  • · Replies 2 ·
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2

Graduate Finding complex solutions to e^x = x

  • marcusmath
  • · Replies 17 ·
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17

Undergrad Real and imaginary parts of an expression

  • Physicslad78
  • · Replies 1 ·
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1

Undergrad What is a Contour Integral and How is it Calculated?

  • Char. Limit
  • · Replies 15 ·
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15

Graduate Checking algebra for triangle inequality with distance to a set

  • Somefantastik
  • · Replies 3 ·
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3

Graduate Hi. Say we want to parametrize the plane R^2.

  • daudaudaudau
  • · Replies 1 ·
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1

Graduate What is the significance of symmetry in the complex plane?

  • lolgarithms
  • · Replies 3 ·
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3

Graduate Problems with identity in complex calc

  • betel
  • · Replies 2 ·
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2

Graduate Differences Between Real and Complex Spherical Harmonics in Signal Rotation

  • Cunicultor
  • · Replies 7 ·
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7

Graduate Solving i^i: Why is i^i = 0.2078?

  • fedaykin
  • · Replies 11 ·
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11

Graduate What is the relationship between feedback and topology in control systems?

  • thrillhouse86
  • · Replies 1 ·
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1

Graduate Can finite metric spaces be embedded into n-dimensional surfaces?

  • Dragonfall
  • · Replies 4 ·
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4

Undergrad How do you determine the cube root of (-1+i) in complex numbers?

  • rpardo
  • · Replies 5 ·
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5

Graduate Solving complex exponential polynomials

  • beechner224
  • · Replies 2 ·
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2

Graduate Continuous Function Outgrowing Polynomial but Not Exponential

  • disregardthat
  • · Replies 4 ·
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4

Graduate Favourite pathological examples

  • fourier jr
  • · Replies 5 ·
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5

Undergrad Imaginary numbers and Imaginary Time

  • TimBowe
  • · Replies 5 ·
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5

Graduate Cauchy sequence without limit in a complete space?

  • LumenPlacidum
  • · Replies 5 ·
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5

Graduate Do nonfaithful functors appear in real colimit constructions?

  • fallgesetz
  • · Replies 1 ·
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1

Graduate Why does (e^{i 2π})^{1/2} give different answers?

  • Proofrific
  • · Replies 12 ·
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12

Graduate Residue of (1 + z)e^(3/z) at an essential singularity

  • joris_pixie
  • · Replies 2 ·
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2

Graduate What's the difference between analytic and continuously differentiable?

  • AxiomOfChoice
  • · Replies 1 ·
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1

Undergrad Can These Two Complex Math Equations Be Solved Correctly?

  • RaYaMe
  • · Replies 3 ·
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3

Undergrad Proof: Solve Rational equation for interval

  • John O' Meara
  • · Replies 4 ·
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4

Undergrad Real root of odd degree polynomial using IVT

  • John O' Meara
  • · Replies 6 ·
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6

Graduate Determining which sets are open?

  • ~Death~
  • · Replies 1 ·
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1

High School Why the point of x + iy would be (x, y) ?

  • I_am_no1
  • · Replies 2 ·
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2

Graduate Convergence of sequences in topological spaces?

  • ~Death~
  • · Replies 4 ·
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4

Graduate Algebraic and topological sets

  • SW VandeCarr
  • · Replies 3 ·
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3

Graduate Does every uncountable set of reals contain an interval?

  • dreamtheater
  • · Replies 3 ·
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3

Undergrad Exponential functions, and complex numbers

  • string_656
  • · Replies 11 ·
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11

Graduate Book Suggestions for Undergraduate Topology Class

  • cap.r
  • · Replies 2 ·
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2

Graduate Duality Pairing and Functionals

  • maros522
  • · Replies 5 ·
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5

Graduate Is the Mandelbrot Set Lebesgue Measurable?

  • Dragonfall
  • · Replies 6 ·
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6

Graduate Isomorphic between plane and line

  • hermitian
  • · Replies 4 ·
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4

Graduate Is There a Stronger Urysohn Lemma for Banach Spaces?

  • quasar987
  • · Replies 2 ·
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2

Graduate Converging Uncountable Sum of Positive Reals

  • Dragonfall
  • · Replies 12 ·
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12

Graduate Continuity & Uniform Continuity: Question on Solutions

  • student12s
  • · Replies 4 ·
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4

Graduate Why is $\mathcal{A} \cup \{0\}$ Compact but $\mathcal{A}$ is Not?

  • lukaszh
  • · Replies 4 ·
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4

Undergrad What Is the Geometric Term for the Cartesian Product of n Unit Intervals?

  • Tac-Tics
  • · Replies 3 ·
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3

Undergrad Problem with Logarithms solutions

  • Jacopo
  • · Replies 2 ·
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2

Graduate W=z^n- transformation in complex space

  • omri3012
  • · Replies 1 ·
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1

Graduate Finding the Right Measure Theory Course for Graduate Studies in Economics

  • mlarson9000
  • · Replies 17 ·
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17

Undergrad To find logarithm of a complex number

  • AlbertEinstein
  • · Replies 19 ·
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19

Graduate Solving a Functional Equation - Muzialis

  • muzialis
  • · Replies 4 ·
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4

Graduate Understanding H=L^2 in Quantum Mathematics

  • pellman
  • · Replies 4 ·
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4

Graduate Can Complex Spaces Be Projected onto Closed Real Spaces without Infinity?

  • thehangedman
  • · Replies 1 ·
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1

Graduate Completeness axiom for subsets of real numbers

  • Bleys
  • · Replies 4 ·
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4

Graduate Understanding Holder's Inequality: A Key Step in Proving Minkowski's Inequality

  • pbandjay
  • · Replies 3 ·
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3

Graduate Definition of open set in topology

  • kof9595995
  • · Replies 9 ·
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9

Graduate What is the formula for complex exponentiation with an irrational exponent?

  • Twinbee
  • · Replies 6 ·
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6

Graduate What is the intuitive meaning of a simply connected region?

  • de_brook
  • · Replies 4 ·
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4

Undergrad Definition of Complex Conjugate

  • Jest3r
  • · Replies 8 ·
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8

Graduate The Euler formula how was it developed?

  • Skynt
  • · Replies 4 ·
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4

Graduate Dividing S^3 into two separate pieces.

  • Spinnor
  • · Replies 1 ·
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1

Graduate Definition of uniform convergence written as math symbols

  • Gerenuk
  • · Replies 17 ·
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17

Graduate Functional Equation for $\sum_{n=0}^{N}n^{k}$

  • zetafunction
  • · Replies 1 ·
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1

Graduate Dirac delta function with complex arguments

  • JayFsd
  • · Replies 2 ·
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2

Graduate Testing if real-valued expressions are negative

  • CRGreathouse
  • · Replies 1 ·
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1

Graduate Foundations of measure theory?

  • tgt
  • · Replies 2 ·
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2

Graduate A strict non-standard inequality .999 < 1

  • Count Iblis
  • · Replies 11 ·
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11

Undergrad Why 1-1/x≠1 even though the limit equals 1

  • greeniguana00
  • · Replies 11 ·
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11