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

High School No distinction between positive and negative for imag nums?

  • Mr Davis 97
  • · Replies 5 ·
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5

Complex numbers simultaneous equations

  • lemonthree
  • · Replies 3 ·
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3

Undergrad Radius of the largest ball inside a complex set.

  • The Bill
  • · Replies 3 ·
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3

High School Predicting outputs of f(x)=(1+i)^x

  • AaronQ
  • · Replies 4 ·
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4

High School Is it possible to represent 1D space within 2D space using only one coordinate?

  • Einstein's Cat
  • · Replies 12 ·
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12

Graduate How can conformal mapping be used to convert curves between different maps?

  • Bruno Tolentino
  • · Replies 7 ·
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7

Undergrad Complex Analysis, holomorphic in circle.

  • kidsasd987
  • · Replies 1 ·
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1

Undergrad A Question about Notation and Continuous Linear Functionals

  • Bashyboy
  • · Replies 4 ·
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4

Undergrad Substitution in a Lebesgue integral

  • DavideGenoa
  • · Replies 7 ·
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7

Undergrad Boundedness and continuous functions

  • orion
  • · Replies 10 ·
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10

Undergrad Is Compactness Necessary for Countable Objects?

  • kidsasd987
  • · Replies 8 ·
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8

Undergrad Understanding the Heine Borel Theorem: An In-Depth Analysis

  • kidsasd987
  • · Replies 3 ·
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3

Undergrad Integral: magnetic field inside infinite cylindrical current

  • DavideGenoa
  • · Replies 9 ·
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9

Graduate Why Is Topology Essential for Understanding Manifolds in GR?

  • Frank Castle
  • · Replies 25 ·
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25

Undergrad Associated Legendre polynomials: complex vs real argument

  • avikarto
  • · Replies 1 ·
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1

Undergrad Why is the Fourier transform of a sinusoid assumed as this?

  • loginorsinup
  • · Replies 4 ·
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4

Undergrad Heine-Borel Theorem shouldn't work for open intervals?

  • Utilite
  • · Replies 9 ·
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9

Undergrad Complex Analysis holomorphic condition

  • kidsasd987
  • · Replies 13 ·
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13

Sigma Algebra: Seeking Help on Closure & Countable Unions

  • Arenholt
  • · Replies 3 ·
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3

Undergrad Complex Analysis Radius of Convergence.

  • kidsasd987
  • · Replies 7 ·
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7

Undergrad Anybody here read Winfree "Geometry of Biological Time"?

  • Jimster41
  • · Replies 6 ·
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6

Undergrad N-dimensional Lebesgue measure: def. with Borel sets

  • DavideGenoa
  • · Replies 2 ·
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2

Undergrad Lebesgue measure under orthogonal transofrmation

  • DavideGenoa
  • · Replies 16 ·
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16

Helpful Tips on Solving Complex Equations

  • fabiancillo
  • · Replies 6 ·
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6

High School Partial derivative of the harmonic complex function

  • Adel Makram
  • · Replies 1 ·
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1

Undergrad Any graph is "drawable" on a 2D surface?

  • paizhaulski
  • · Replies 3 ·
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3

Undergrad Any two polygons can be continuously "extended" or ....?

  • paizhaulski
  • · Replies 1 ·
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1

High School What is a clopen set and how can a set be both open and closed?

  • ProfuselyQuarky
  • · Replies 20 ·
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20

Undergrad Analytic functions of analytic functions

  • Physgeek64
  • · Replies 3 ·
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3

Undergrad Graphs of inverse trigonometric vs inverse hyperbolic functions

  • Happiness
  • · Replies 1 ·
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1

Graduate Convergence of a cosine sequence in Banach space

  • Jaggis
  • · Replies 13 ·
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13

Undergrad Why is E(t) multiplied by e^(-ix) in Plancherel's Theorem proof?

  • QuantumDuality
  • · Replies 3 ·
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3

Graduate Concept of duality for projective spaces and manifolds

  • SVN
  • · Replies 8 ·
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8

High School Can Riemann zeta function be written as ##f(s)=u(s)+iv(s)##?

  • Adel Makram
  • · Replies 1 ·
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1

High School Simplifying the factors of a complex number's imaginary part

  • TheCanadian
  • · Replies 2 ·
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2

Graduate Fourier Transform of a 2D Anisotropic Gaussian Function

  • Mahpak
  • · Replies 1 ·
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1

Graduate Why are conics indistinguishable in projective geometry?

  • SVN
  • · Replies 6 ·
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6
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3

Integrating by an other variable

  • evinda
  • · Replies 1 ·
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1

Undergrad What Is the Correct Expansion of \( e^{\frac{1}{z-1}} \)?

  • bananabandana
  • · Replies 15 ·
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15

Efficient Method for Extracting Square Root of Complex Expressions

  • NotaMathPerson
  • · Replies 7 ·
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7

High School Which Branch of Math Should I Study for a Foundation in Functional Analysis?

  • houlahound
  • · Replies 4 ·
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4

Undergrad General topology: Countability and separation axioms

  • beep300
  • · Replies 6 ·
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6

Graduate Can Gamma Functions Be Evaluated Analytically for Non-Integer Values?

  • LagrangeEuler
  • · Replies 2 ·
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2

Graduate On embeddings of compact manifolds

  • fresh_42
  • · Replies 2 ·
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2

Undergrad Tiling Polygons: Can Any n-Sided Polygon Tile?

  • thetexan
  • · Replies 1 ·
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1

Graduate Density of Irrational Numbers in [0;1]

  • Calabi
  • · Replies 4 ·
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4

Undergrad Relaxed conditions for the density: Ampère's law still valid?

  • DavideGenoa
  • · Replies 10 ·
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10

Using the Definition: Showing $u \in C^0 [0,1]$

  • evinda
  • · Replies 2 ·
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2

Undergrad Imaginary sinusoidal exponential

  • spaghetti3451
  • · Replies 8 ·
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8
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2

High School What is the definition of a plane?

  • thetexan
  • · Replies 14 ·
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14

Proving the Existence of Constants in a Summation Inequality

  • evinda
  • · Replies 14 ·
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14

The function is 0 almost everywhere

  • evinda
  • · Replies 1 ·
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1

Undergrad Struggling with Moduli in Complex Numbers?

  • SamitC
  • · Replies 4 ·
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4

Undergrad Triangulation of circle and disk in R2

  • pierce15
  • · Replies 17 ·
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17

High School Is 0 a Real Number, an Imaginary Number, or Both?

  • Isaac0427
  • · Replies 36 ·
2
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36

So, the final answer would be 0. Is that correct?

  • evinda
  • · Replies 4 ·
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4

Is It Possible to Prove the Complex Number Challenge?

  • Greg
  • · Replies 11 ·
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11

Undergrad Why the space X=(0,1) is (not sequentially) compact?

  • santiagorf
  • · Replies 7 ·
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7

Proof of Fredholm-Volterra Equation Convergence

  • sarrah1
  • · Replies 1 ·
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1

Define a discontinuous sine function?

  • samir
  • · Replies 2 ·
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2

Real conjugates of complex numbers?

  • samir
  • · Replies 1 ·
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1

Undergrad Physical implications from Vitali sets or Banach-Tarski?

  • greypilgrim
  • · Replies 14 ·
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14

High School Can Complex Numbers Extend Beyond Two Dimensions?

  • thetexan
  • · Replies 5 ·
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5
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3
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1

Graduate A function whose integral is either 0 or 1

  • friend
  • · Replies 3 ·
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3

Undergrad How Does Jackson's Use of Manifolds Enhance Understanding of Electrodynamics?

  • kidsasd987
  • · Replies 4 ·
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4

A whole function approximating polynomials

  • LWRS
  • · Replies 1 ·
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1

Graduate Functional equation f(x)^n f(a - x) = 1

  • Jonas Hall
  • · Replies 4 ·
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4

Undergrad Cantor's intersection theorem (Apostol)

  • mr.tea
  • · Replies 2 ·
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2

Does this count as a proof for the infimum?

  • NoName3
  • · Replies 2 ·
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2

Find GLB of A: $(-1)^n\left(\frac{1}{4}-\frac{2}{n}\right)$

  • NoName3
  • · Replies 5 ·
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5

Graduate Can Discrete Parameters Be Used in Limit Calculations?

  • friend
  • · Replies 39 ·
2
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39

High School Is hοh Monotonic If h Is Continuous?

  • anachin6000
  • · Replies 4 ·
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4

Is the Product of Real Numbers Always Larger When Exponentiated?

  • NoName3
  • · Replies 2 ·
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2

Prove Lagrange Property w/ Algebra - A Hint for You!

  • evinda
  • · Replies 3 ·
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3

Using the axioms of ordered field

  • NoName3
  • · Replies 2 ·
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2

Proving Subsets of Intervals in $\mathbb{R}$

  • NoName3
  • · Replies 2 ·
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2

Undergrad Why Does Weak-* Topology Use Finite Neighborhoods?

  • strangerep
  • · Replies 53 ·
2
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53

Residue Calc: $\cot^n(z)$ at $z=0$

  • polygamma
  • · Replies 1 ·
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1

Graduate The fundamental group of preimage of covering map

  • 1591238460
  • · Replies 5 ·
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5

Undergrad Partitions of Euclidean space, cubic lattice, convex sets

  • Martin Rattigan
  • · Replies 2 ·
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2

Undergrad Non unicity of decimal expansion and extremes of intervals

  • DaTario
  • · Replies 54 ·
2
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54

Graduate Commutations and delta in deriving Ampère's law

  • DavideGenoa
  • · Replies 2 ·
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2

Graduate Commutation integral/derivative in deriving Ampère's law

  • DavideGenoa
  • · Replies 20 ·
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20

What Does the Branch of the Cube Root Function Mean?

  • alexmahone
  • · Replies 1 ·
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1

Graduate Question about proof from Bishop & Goldberg

  • TeethWhitener
  • · Replies 11 ·
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11

Graduate Charts on Topological Manifolds - Simple Notational Issue

  • Math Amateur
  • · Replies 2 ·
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2

How Do You Calculate the Contribution of Each Element to Total Variance?

  • Rubberneck
  • · Replies 1 ·
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1

Graduate Convex Vector Spaces: Does Sum Exist in Normed Vectorial Space?

  • Calabi
  • · Replies 4 ·
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4

Complete Sets of Real Numbers: Find All

  • Evgeny.Makarov
  • · Replies 2 ·
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2

Graduate Clarification: proof that perfect subsets of R^k uncountable

  • cpsinkule
  • · Replies 6 ·
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6

Graduate Understanding the Purpose of Charts in Differential Geometry

  • Fgard
  • · Replies 7 ·
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7

Find Max Function g: $\sqrt{10^{2016}}$

  • evinda
  • · Replies 2 ·
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2

Graduate Find Real Value of sin(i) Without i

  • TheCanadian
  • · Replies 3 ·
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3

Graduate Is Isometry the Same as Isomorphism?

  • ericm1234
  • · Replies 9 ·
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9

Undergrad Proof that the world is not flat

  • Whitehole
  • · Replies 73 ·
3
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73
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1