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 $\ell^\infty$ a Compact Metric Space?
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Graduate Does T have a unique fixed point in X?
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MHB Best wishes :)Question: How do we use supremum in the proof of Cauchy sequence?
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MHB Proving $T:X\to X$ is not a Contraction on $X=[1, \infty)$
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Graduate Complex Mapping - Is transforming boundaries enough?
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MHB What is the limit of a circumference as the power approaches infinity?
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Graduate ##\int \frac{dz}{z} ## along a line on the complex plane
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Graduate A path which its domain is a general compact set.
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MHB Cauchy sequence in fixed point theory
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MHB Non Increasing and Decreasing Sequence
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MHB Is Non-Increasing the Same as Decreasing?
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MHB Increasing, non-increasing, decreasing and non-decreasing functions
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Undergrad What does the term "pointwise" refer to?
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Graduate Learning Topology: Problem Solving & Book Recommendations
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Undergrad Why Do Algebraic Continuity Theorems Confuse Me?
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Graduate Distributions on non-test functions
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Graduate Distributions & test functions in specific applications
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Graduate What is the intuitive meaning of continuity in topology?
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Graduate Proving the Limit of a Sequence is Unique: Real Analysis Class
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MHB Proof of Supremum of $M$ Mapping into Itself
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Graduate Points on a Plane: Representation with 1 or 2 Real Numbers?
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MHB Generalization of Banach contraction principle
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MHB Contraction constant in banach contraction principle
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MHB Continuous mapping and fixed point
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MHB Proof of Banach-Caccioppoli theorem
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MHB Proof of Contraction Mapping for $f\left(x\right)={e}^{{-e}^{-x}}$
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Undergrad Define the complex number Z = u^v
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Undergrad Complex numbers and negative roots
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Graduate Confusion about definition of compactness
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Graduate Why isnt Cauchy's formula used for the perimeter of ellipse?
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Undergrad Complex numbers and beyond....
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MHB Show Metric Proves All Points Inside Circle Have Same Center
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MHB Please check Residue theorem excercise
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Undergrad How Many Spanning Trees Can a Graph Have?
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Graduate What is a derivative in the distribution sense?
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Graduate Is Category Theory Really Useless for Building Versatile Scientific Models?
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Graduate Does Bott periodicity imply homotopy equivalences?
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MHB Proof of Cauchy Integral formula
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MHB Zero Integral Implies Zero Function
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MHB Generalized triangle inequality in b-metric spaces
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MHB Triangle inequality in b-metric spaces
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MHB Find coefficiant of Laurent series, without using residue
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Graduate Sufficient condition for the density
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MHB Finding Complex Roots: Poles of $ \frac{1}{{z^4}+4} $, {z: |z-1| LE 2}
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MHB Please check find residue problem
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Graduate Are all smooth functions square-integrable?
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Graduate Entire Functions and Lacunary Values.
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MHB Why Is the Existence of m and n Guaranteed in the Cauchy Sequence Proof?
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MHB Path dependance of complex conjugate
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MHB Understanding the Laurent Series of $\frac{1}{z(z-1)(z-2)}$
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Graduate How does this statement follow? (adjoints on Hilbert spaces)
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Graduate What happens when two identical one-sided objects are merged in space?
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Graduate What is the Nature of Singularity in the Function f(x)=exp(-1/z)?
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MHB Cauchy Integral Theorem with partial fractions
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Graduate How does one-to-oneness follow from this?
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High School I think I'm missing something in this complex number problem
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Graduate How does the idea of entropy relate to something like E8
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Undergrad Proof of Infinite Set of Real Numbers Between Two Unequal Real Numbers
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Graduate Why my endomorphisme between Polynomial fonction is not continuous?
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MHB Intuition for inverse hyperbolics
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MHB 1st Derivative of Cauchy Integral formula
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MHB Contour integral representation of Kronecker delta
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MHB Reverse direction for complex functions
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Undergrad Is a Perfect Circle Possible Given the Limitations of Pi and Space?
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MHB Tricky Complex number simplification
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MHB Why is a complex function analytic if it has a non-zero imaginary component?
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Graduate Group theory? This solution doesn't make sense....
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Graduate Understand Successive Bisection for Theorem Proof
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Undergrad Fundamental theorem of algebra and factoring?
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MHB Reverse triangle inequality with a + sign
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MHB Do Cauchy-Riemann Conditions Guarantee Analyticity?
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Graduate Solve Endomorphism Sequence Questions in a Vectoriel Space
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MHB Understanding the Concept of Double Conjugate in Complex Functions
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Graduate Question on dense subset of l^p space
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Graduate Questioning an assumption in calculus of variations
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Undergrad Mathematical insight about waves
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Graduate Fourier Series: Understanding Non-Periodic Signals
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MHB Proving d(x,A) ≤ d(x,y) + d(y,A) in Metric Spaces
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Graduate Weierstrass p-Function Asympototics?
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MHB Find Roots of sin z: Solutions & Explanations
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MHB Outer measure exclusion of zero set question
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Graduate Nonlinear constrained optimization - how?
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Undergrad Why are Real Numbers Often Referred to as Points in Mathematical Functions?
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Graduate Real part of this complex quantity
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MHB Prove sinh(z) Identity: Show |sinh(z)|^2 = sin^2x + sinh^2y
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Graduate Motivation of sin and cos functions
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Graduate Rigorousness of this Dirac delta formula
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Graduate How many topologies exist on 4 points? Any nomenclature?
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Graduate Question about a flat torus topology
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Graduate ....they say it's very difficult to show what sqrt2 is....
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Graduate Evaluating a limit of a function of two variables
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MHB Example of right upper semicontinuous function
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MHB How can the complex exponential product be proven for all real p and m?
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Graduate Understanding // in the Hint for Showing Numbers of Form ±m√2/n Are Dense
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Graduate Transversal Intersection of More than 2 Surfaces
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MHB Fixed Point Theorem & Contractive Maps
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Graduate Basic questions on Nakahra's definition of topological space
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Graduate Smallest subspace of a vector space
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MHB Why is the contraction constant important in the Banach contraction principle?
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MHB What Is the Relation Between \( x(n) \) and \( X(f) \) Given \( f = kn \)?
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