Topology and Analysis Forum

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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.
Graduate General question regarding continuous functions and spaces
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MHB How Does Complex Analysis Explain the Integral of Sin^2(x)/x^2?
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Graduate Invariance of Domain: Showing U Open in Differential Geometry | Spivak Ch.1
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MHB Show a certain sequence in Q, with p-adict metric is cauchy
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Graduate What kind of math notation is this?
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MHB Improper complex integrals--residue
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Graduate Is my understanding of open sets and bases in topology correct?
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MHB Proving Uniqueness of Fourier Coefficients for Continuous Periodic Functions
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MHB Circle radius 2 oriented counterclockwise
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MHB Number of Zeros Inside Unit Circle for Polynomial P(z)
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Graduate Proving the Validity of a New Metric Space
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MHB Proving Convergence of e^z Series Using Ratio Test on Coefficients
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MHB Solving $z^4=-1$ with a Complex Number
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MHB Analyzing the Complex Function $g(z)$
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MHB How is the Steepest Descent Formula Used to Solve Linear Systems?
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MHB Complex Numbers III: Solving z^5-(z-i)^5=0
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Graduate Help me parse the logic of this statement
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MHB Inf{frac{n*sqrt(3)} : n in integer}=0
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Graduate Whats an infinite intersection of open sets
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MHB What is the Integral of a Function Around a Rectangle Oriented Clockwise?
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Graduate What Is the Boundary of a Product Manifold?
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MHB Convergence of Ratio Test for Complex Numbers z in C
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MHB Quick question about continuous mapping
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MHB Integrating $\tan z$ Around a Circle of Radius 8
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Graduate Cardinality of the Preimage f^{-1}(y) of f:X->Y continuous?
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MHB Solve for Complex Number \(z\) Given \(4+i(4z+1)=2re^{i(\pi+\theta)}\)
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MHB A Quick Question About Orthornomal Systems of Functions and Fourier Series
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MHB Fourier Transform: Proving $G(z)$ is an Entire Function
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MHB Find the Modulus & Argument of \(wz\)
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Graduate Glueing together normal topological spaces at a closed subset
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Graduate Closed set as infinite intersection of open sets
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MHB Is My Complex Integral Calculation Correct?
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MHB Problem 9 section 3.3 from Bartle
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MHB Well-Definedness and C^Infinity Closure of Convolutions
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MHB Surjectivity of an Isometry given the metric space is complete.
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MHB How Do You Calculate the Limit of M*exp(D*exp(c*t)) as t Approaches Infinity?
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MHB Is f Holomorphic on D if and only if p_g = 0 on D?
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MHB Residue Theorem: Find Residue at 0 for e^z/z^3
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Graduate Julia Sets: Periodic and Non-Periodic Points Explained
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MHB Finding values for a harmonic function
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MHB Proving No Simple Pole at 0 for $f'$ on $\mathbb{D} - \{0\}$
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MHB A guide to Calculating the Laurent Series of $\frac{33}{(2z - 1)(z + 5)}$
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MHB Find Laurent Series for $\frac{1}{z^2(1 - z)}$ in $0 < |z| < 1$ & $|z| > 1$
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Graduate From continuity to homeomorphism, compactness in domain
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MHB Does a_n Converge to Zero Given b_n Approaches Zero and a_n/b_n Approaches L?
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Graduate Is Boundedness Applicable to Topological Spaces?
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MHB Solve Riemann Integral: Show \( \int_a^b f = \lim U_n = \lim L_n \)
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Undergrad Open Set Image: Is Constant Function's Image Open?
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MHB What is Arzela's Lemma in Fichtengoltz's Book?
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Undergrad Does Sequence (n,1/n) Converge or Diverge?
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Graduate How to prove that a topological space is non-hausdorff?
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Graduate Clopen Sets: Closure = Interior?
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MHB Holomorphic Function Continuity and Holomorphicity on Real Interval [2,5]
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Graduate Is a Space Connected if Its Closure Is Connected?
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MHB Understanding Normed Linear Spaces: Convergence in C[0,1]
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MHB Proving Continuity of $$ \int_{-\pi}^{\pi}te^{xt}\cos(yt)g(t)dt$$
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Graduate Can the Superior Limit of a Sequence Be Lower Than Its Supremum?
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Graduate Is This a Valid Topology on [0, ∞)?
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MHB Is the Triangle Inequality Valid for Natural Numbers and Complex Numbers?
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MHB Uniform Convergence of f{_n} in Complex Analysis on S=[0,infinity)
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MHB What is Problem 167 in Serge Lang's Complex Analysis about?
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Graduate Definition of a Topological Space
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MHB Is this approach to evaluating a complex integral valid?
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MHB Testing Uniform Convergence of Complex Function Sequences with Natural Numbers
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MHB N th root of a positive number is positive ....
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MHB What is the Limit of the Sequence Defined by \( z_{n+1}=\sqrt{a+z_n} \)?
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Graduate Are all open sets compact in the discrete topology?
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MHB Complex integration no Residue Theory everything else is ok
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MHB Analytic Functions on the Unit Disc
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MHB How to Express Cauchy Integral Formula in Terms of a Power Series?
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MHB Convergence Condition for Applying Ratio Test to Power Series
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High School Can someone help with Argand plane graphing and finding the radius?
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MHB Prove Limit of |a_n|^(1/n) = L
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MHB Is the Series $\displaystyle\sum\frac{\sin n}{n}$ Absolutely Convergent?
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MHB Proof of Winding Number 1 for Analytic $f$
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MHB Is the Sequence \(X\) Convergent or Bounded?
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MHB I guess it will be the same as i,1-i
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Undergrad What is the difference between the phase and argument of a complex number?
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MHB Complex Integral: $\int_0^1$ Calculation
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MHB Circle radius 2 complex integration
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MHB Primitive e^z/z Gamma: Finding the Integral
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MHB Finding the Primitive of a Complex Integral
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Graduate Is the Sum of Two Elements in a Convex Compact Subset of R^2 Also in the Subset?
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MHB Absolute Convergence: Proving $\sum a_n$ is Convergent
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MHB SE Class 12 Maths Alternating Series Test
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Undergrad How to tell that 1/(z+2i) is not analytic?
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MHB Does the Converse of the Ratio Test Always Hold for Convergent Series?
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MHB Convergence of $\displaystyle\sum\frac{n^5}{2^n}$
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MHB Solving Attached Problem, Plus MHF Update
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MHB When does the series $\sum_2^\infty\frac{1}{n(\ln n)^p}$ diverge for $p<0$?
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MHB Does the series $\sum_1\sin\left(\frac{1}{n}\right)$ converge?
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MHB Is the Absolute Convergence Theorem Sufficient to Prove This?
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Graduate Weakly sequentially compact supsets
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Graduate Is an Open Interval Homeomorphic to R?
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Undergrad Complex conjugate of absolute exponential
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MHB Struggling with Fourier Transform Eigenvalues?
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MHB Complex integral oriented counterclockwise
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MHB Evaluating Complex Integration I_c |z^2|
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MHB Power Series Expansion: Solving for 1/1+z at z=-5 with Radius of Convergence
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MHB Show that C.R conditions are held.
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