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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What Is the Correct Form of a Holomorphic Function on \(\mathbb{C}-\{0\}\)?
- Dustinsfl
- · Replies 1 ·
Graduate Difference between hilbert space,vector space and manifold?
- aditya23456
- · Replies 9 ·
Undergrad Are Finite Sets and the Set of All Integers in R^2 Closed?
- jwqwerty
- · Replies 12 ·
Prove $f(x)=Cx$ for All $x$: Functional Equation
- alexmahone
- · Replies 5 ·
Graduate Do primes exist in the complex numbers?
- Dashin
- · Replies 9 ·
Graduate Can a Complex Plane Applet Graph xx = i?
- Frogeyedpeas
- · Replies 1 ·
Graduate Definition of Limit Point: Is There a Point Not in E?
- jwqwerty
- · Replies 5 ·
Hyperbolic functions
- CaptainBlack
- · Replies 1 ·
Trig integration complex analysis
- Dustinsfl
- · Replies 4 ·
Integration--Cauchy Principal Value, Residue, line integration, poles
- Dustinsfl
- · Replies 5 ·
Give an example of a convergent series
- alexmahone
- · Replies 2 ·
Subsequence - absolute convergence
- alexmahone
- · Replies 2 ·
Graduate Continuity of piecewise functions when f and g agree on A
- TwilightTulip
- · Replies 1 ·
How Does Complex Analysis Explain the Integral of Sin^2(x)/x^2?
- Dustinsfl
- · Replies 9 ·
Graduate Why does invariance of domain theorem apply to open sets homeomorphic to Rn?
- Rasalhague
- · Replies 4 ·
Show that s_n = Σ(t_k * p^k) is Cauchy in the p-adic metric
- arturo_026
- · Replies 1 ·
Graduate What kind of math notation is this?
- muffinman123
- · Replies 3 ·
Improper complex integrals--residue
- Dustinsfl
- · Replies 2 ·
Graduate Is my understanding of open sets and bases in topology correct?
- Question Man
- · Replies 2 ·
Proving Uniqueness of Fourier Coefficients for Continuous Periodic Functions
- Markov2
- · Replies 2 ·
Circle radius 2 oriented counterclockwise
- Dustinsfl
- · Replies 2 ·
Number of Zeros Inside Unit Circle for Polynomial P(z)
- Dustinsfl
- · Replies 7 ·
Graduate Proving the Validity of a New Metric Space
- Lily@pie
- · Replies 8 ·
Proving Convergence of e^z Series Using Ratio Test on Coefficients
- Poirot1
- · Replies 6 ·
Solving $z^4=-1$ with a Complex Number
- Dustinsfl
- · Replies 5 ·
Does g(z) have the same zeros as f(z) by Rouché's theorem?
- Dustinsfl
- · Replies 3 ·
How is the Steepest Descent Formula Used to Solve Linear Systems?
- Amer
- · Replies 1 ·
Complex Numbers III: Solving z^5-(z-i)^5=0
- Punch
- · Replies 3 ·
Graduate Parsing the definition of residue as existence of a primitive
- Poopsilon
- · Replies 2 ·
Prove inf{frac(n√3) : n ∈ Z+} = 0
- caffeinemachine
- · Replies 11 ·
Graduate Whats an infinite intersection of open sets
- natasha d
- · Replies 8 ·
What is the Integral of a Function Around a Rectangle Oriented Clockwise?
- Dustinsfl
- · Replies 1 ·
Graduate What Is the Boundary of a Product Manifold?
- mma
- · Replies 9 ·
Convergence of Ratio Test for Complex Numbers z in C
- Dustinsfl
- · Replies 5 ·
Continuity of f on subset E vs. continuity at each point in E
- arturo_026
- · Replies 1 ·
Integrating $\tan z$ Around a Circle of Radius 8
- Dustinsfl
- · Replies 5 ·
Graduate Cardinality of the Preimage f^{-1}(y) of f:X->Y continuous?
- Bacle2
- · Replies 8 ·
Solve for Complex Number \(z\) Given \(4+i(4z+1)=2re^{i(\pi+\theta)}\)
- Punch
- · Replies 14 ·
Fourier series divergence and completeness of {e^inx} in L²
- TaylorM0192
- · Replies 1 ·
Fourier Transform: Proving $G(z)$ is an Entire Function
- Dustinsfl
- · Replies 6 ·
Finding modulus and argument of wz given w and z in polar form
- Punch
- · Replies 2 ·
Graduate Glueing together normal topological spaces at a closed subset
- conquest
- · Replies 4 ·
Graduate Closed set as infinite intersection of open sets
- lonewolf5999
- · Replies 4 ·
Is My Complex Integral Calculation Correct?
- hmmmmm
- · Replies 2 ·
Problem 9 section 3.3 from Bartle
- issacnewton
- · Replies 10 ·
Well-Definedness and C^Infinity Closure of Convolutions
- TaylorM0192
- · Replies 2 ·
Surjectivity of an Isometry given the metric space is complete.
- arturo_026
- · Replies 1 ·
How Do You Calculate the Limit of M*exp(D*exp(c*t)) as t Approaches Infinity?
- charlottewill
- · Replies 1 ·
Is f Holomorphic on D if and only if p_g = 0 on D?
- Stephen88
- · Replies 2 ·
Residue Theorem: Find Residue at 0 for e^z/z^3
- Dustinsfl
- · Replies 4 ·
Graduate Why do Julia sets contain non-periodic points if they're defined by periodic points?
- Kortirion
- · Replies 1 ·
Finding values for a harmonic function
- Stephen88
- · Replies 2 ·
Proving No Simple Pole at 0 for $f'$ on $\mathbb{D} - \{0\}$
- Dustinsfl
- · Replies 7 ·
Laurent series of 33/((2z-1)(z+5)) about z = -3i
- Dustinsfl
- · Replies 2 ·
Laurent series for 1/(z²(1-z)) in two regions
- Dustinsfl
- · Replies 1 ·
Graduate From continuity to homeomorphism, compactness in domain
- jostpuur
- · Replies 2 ·
Does a_n Converge to Zero Given b_n Approaches Zero and a_n/b_n Approaches L?
- alexmahone
- · Replies 2 ·
Graduate Is Boundedness Applicable to Topological Spaces?
- blahblah8724
- · Replies 1 ·
Solve Riemann Integral: Show \( \int_a^b f = \lim U_n = \lim L_n \)
- Fantini
- · Replies 2 ·
Undergrad Open Set Image: Is Constant Function's Image Open?
- zendani
- · Replies 9 ·
What is Arzela's Lemma in Fichtengoltz's Book?
- Also sprach Zarathustra
- · Replies 1 ·
Undergrad Does Sequence (n,1/n) Converge or Diverge?
- zendani
- · Replies 6 ·
Graduate How to prove that a topological space is non-hausdorff?
- AdrianZ
- · Replies 5 ·
Graduate Clopen Sets: Closure = Interior?
- blahblah8724
- · Replies 9 ·
Holomorphic Function Continuity and Holomorphicity on Real Interval [2,5]
- Dustinsfl
- · Replies 6 ·
Graduate Is a Space Connected if Its Closure Is Connected?
- blahblah8724
- · Replies 4 ·
Understanding Normed Linear Spaces: Convergence in C[0,1]
- bugatti79
- · Replies 2 ·
Proving Continuity of $$ \int_{-\pi}^{\pi}te^{xt}\cos(yt)g(t)dt$$
- Dustinsfl
- · Replies 8 ·
Graduate Can the Superior Limit of a Sequence Be Lower Than Its Supremum?
- IniquiTrance
- · Replies 2 ·
Graduate Intersection of (a, ∞) sets in a topology on [0, ∞)
- blahblah8724
- · Replies 2 ·
Is the Triangle Inequality Valid for Natural Numbers and Complex Numbers?
- Dustinsfl
- · Replies 4 ·
Uniform Convergence of f{_n} in Complex Analysis on S=[0,infinity)
- Poirot1
- · Replies 3 ·
What is Problem 167 in Serge Lang's Complex Analysis about?
- Dustinsfl
- · Replies 3 ·
Graduate Definition of a Topological Space
- Jamma
- · Replies 3 ·
Is this approach to evaluating a complex integral valid?
- polygamma
- · Replies 1 ·
Testing Uniform Convergence of Complex Function Sequences with Natural Numbers
- Poirot1
- · Replies 1 ·
Proving the nth root of a positive number is positive
- issacnewton
- · Replies 4 ·
What is the Limit of the Sequence Defined by \( z_{n+1}=\sqrt{a+z_n} \)?
- issacnewton
- · Replies 7 ·
Graduate Are all open sets compact in the discrete topology?
- Useful nucleus
- · Replies 9 ·
Complex integration no Residue Theory everything else is ok
- Dustinsfl
- · Replies 5 ·
Analytic Functions on the Unit Disc
- Dustinsfl
- · Replies 7 ·
How to Express Cauchy Integral Formula in Terms of a Power Series?
- Dustinsfl
- · Replies 10 ·
Convergence Condition for Applying Ratio Test to Power Series
- alexmahone
- · Replies 2 ·
High School Finding resources for complex number geometry and Argand diagrams
- AlchemistK
- · Replies 6 ·
Prove Limit of |a_n|^(1/n) = L
- alexmahone
- · Replies 7 ·
Is the Series $\displaystyle\sum\frac{\sin n}{n}$ Absolutely Convergent?
- alexmahone
- · Replies 2 ·
Proof of Winding Number 1 for Analytic $f$
- Dustinsfl
- · Replies 2 ·
Is the Sequence \(X\) Convergent or Bounded?
- issacnewton
- · Replies 9 ·
I guess it will be the same as i,1-i
- AkilMAI
- · Replies 2 ·
Undergrad What is the difference between the phase and argument of a complex number?
- eggshell
- · Replies 1 ·
Computing ∫₀¹ (2t+i)/(t²+it+1) dt
- Dustinsfl
- · Replies 17 ·
Circle radius 2 complex integration
- Dustinsfl
- · Replies 11 ·
Primitive e^z/z Gamma: Finding the Integral
- Dustinsfl
- · Replies 8 ·
Finding the Primitive of a Complex Integral
- Dustinsfl
- · Replies 3 ·
Graduate Is the Sum of Two Elements in a Convex Compact Subset of R^2 Also in the Subset?
- almostsure
- · Replies 1 ·
Absolute Convergence: Proving $\sum a_n$ is Convergent
- alexmahone
- · Replies 5 ·
SE Class 12 Maths Alternating Series Test
- alexmahone
- · Replies 19 ·
Undergrad How to tell that 1/(z+2i) is not analytic?
- nutcase21
- · Replies 3 ·
Does the Converse of the Ratio Test Always Hold for Convergent Series?
- alexmahone
- · Replies 5 ·
Convergence of $\displaystyle\sum\frac{n^5}{2^n}$
- alexmahone
- · Replies 3 ·