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.
MHB Is $|f(\theta)|$ less than or equal to the sum of the absolute values of $A_n$?
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MHB How to Solve the Heat Problem in the Disk using Fourier Series?
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Using the residue theorem to evaluate a real integral.
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MHB On the Implication of Addition Axioms
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Closed and open at the same time?
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Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?
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MHB Closed sets intersection of countable open sets
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MHB Accumulation Points of $(-1)^n + (1/m)$: Is it True?
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A question on the orthogonal polynomial
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Understanding lim sup and lim inf: Finding limit points and subsequential limits
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MHB Exploring the Accumulation Points of $1/n$
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MHB Exploring the Series $(-1)^n/[1 + (1/n)]$ for All Positive Integers $n$
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MHB Complex accumulation points and open/closed
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MHB Accumulation Points of Rationals: Explained
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MHB R^2 accumulation and open/closed
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Defining an upper/lower bound in lexicographically ordered C.
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MHB Solving Even Function Integrals: $a_0$ & $a_n$
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Domain and range of complex functions
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MHB Calculating Fourier Coefficients for $f(\theta) = \theta^2$ on $[-\pi, \pi]$
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MHB Understanding a question Fourier series
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MHB Fourier Coefficients for $f(\theta) = \theta$
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MHB Calculating Fourier Series of $f(\theta)$ on $[\pi, -\pi]$
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MHB Proof: if f holomorphic then f(z)=λz+c
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Bad proof in Fomin's Calculus of Variations?
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MHB Is $f$ a one-to-one function on $S$?
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Open sets preserved in linear transformation that isn't bijective?
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MHB Are There Infinitely Many Rational Numbers Between Two Irrational Numbers?
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What is the limit of (ah-1)/h as h approaches 0?
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MHB Special cases for sine and cosine sum
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Exploring the Basel Problem: Proving pi*pi/12
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Is the Nested Interval Theorem Flawed in My Textbook?
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MHB Proving $\sum_{k=1}^{n}e^{ik\theta}$ Formula
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Are Sigma Algebras Unique for a Given Set?
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MHB Supremum and Infimum of $S$: $a < b < c < d$
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MHB Trig identities Fourier Analysis
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Proving a known proof involving injection.
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Understanding Function Notation in Higher Level Mathematics
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Spivak Exercice, Least Upper Bounds Chapter, Proof
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MHB Proving the Polynomial Identity for Dividing a^n-b^n by a-b
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MHB Proving Sum of Cosines Simplifies to Trig Identity
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MHB Proving the Basic Identity of Fourier Series
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Topology, functional analysis, and group theory
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Proof Error Q. Conway's Functions of One Complex Variable VI
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MHB Singularities of Complex Functions
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Proof of Lagrange multipliers method in calculus of variations.
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The least upper bound property and the irrationals.
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Precise definition of the limit of a sequence
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Understanding K-Convexity: Visualization and Intuitive Explanation
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Does Unconditional Convergence Apply to Infinite Subseries Partitions?
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Cardinalic flaw of Riemann integral
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Showing Closed Subsets of Compact Sets are Compact
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The role of the Jacobian in the Implicit Function Theorem
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What is Semidifferential Calculus?
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Calculus of Variation on Local Regions of Function Space
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Exploring the Cantor Set: Why There Are No Interior Points
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Why Can't a Sequence Have Two Distinct Limits in a Metric Space?
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Is a Concave, Nondecreasing, and Bounded Function on [0, ∞) Always Continuous?
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Apply Lebesgue Integral: Examples & Explanations
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Playing with Analytical Operators
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Q is dense in R question about proof
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An algebraic property of complex numbers
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Conditional vs unconditional convergence
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Why Parseval's Identity Fails for Higher Exponents in Basel Problem
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An Intuitive Understanding Vs. Analytic Proofs
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Rudin Thm 2.41: E Closed & Bounded if Every Inf Subset Has a Lmt Pt
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Is it Possible for a Closed Disk to be Contained in an Open Set?
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Homeomorphisms with the discrete topology
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Difference between theorems 2.12 & 214 of Baby Rudin
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MHB Lambert W Function: Solving $r=ue^u$
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Dirac delta function, change of variable confusion
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Sequence in Hilbert space,example
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MHB What is the error bound in cubic spline approximation?
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MHB Complex Number Loci: Proof and Circle Variation with z = 1/(3+it)
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Does this condition imply f:R^2->R is continuous?
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Measurable and Unif. Convergence in (a,b)
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MHB Fourier series, pointwise convergence, series computation
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Geometric difference between a homotopy equivalance and a homeomorphism
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Changes in the internal structure during a Topological transform
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MHB Understanding Riemann Integrals of $\ln\ x$
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Axiom of Choice and Metric Spaces.
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If every basic open cover has a countable subcover
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MHB Finding the Laurent series for $f(z)$ in an annulus containing $z = 2$
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Is There a Faster Way to Prove Part (b) Using Radon-Nykodim?
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Continuity of one Norm w.resp. to Another. Meaning?
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Point Set Topology: Why A={1/n:n is Counting Number} is Not a Closed Set?
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Can Nested Summations and Products Be Simplified?
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MHB To prove a series of function is bounded
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Using Rolle's Theorem to Find the Zeros of a Function
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Question on Rudin Theorem 3.44 Inequality
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What is the Cauchy Product Formula in Power Series?
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Rudin Theorem 3.23: Proving the Limit of Terms is Zero
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Formal definition of derivative: trig vs non trig functions
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Applying Reynold's Theorem to Infinitesimal Element: Fluid Dynamics
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Understanding Measure Theory with Rudin's Principles of Mathematical Analysis
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Common assumption in proof for Inverse function theorem
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MHB Proving T is Continuous in a Complex Banach Space
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Closed subspace of a Lindelöf space is Lindelöf
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MHB Is this power series a convergent series?
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Tangent space as best approximation
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MHB Proving That f Є R(V) When f Є R(α)
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Topology and Analysis

Welcome to the Topology forum!

Topology and analysis are two branches of mathematics that investigate the properties of spaces and functions, respectively. Topology is concerned with the study of the properties that remain unchanged under continuous deformations, such as stretching or bending, but not tearing. It explores concepts like continuity, connectedness, and compactness.

Analysis, on the other hand, is focused on understanding the behavior of mathematical functions and sequences. It deals with limits, continuity, differentiation, and integration, providing tools for a detailed examination of functions. Both topology and analysis play integral roles in diverse areas of mathematics and find applications in various scientific and engineering disciplines.

Together, they contribute to a deeper understanding of the structure and properties of mathematical objects.
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