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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Undergrad Convexity of a function I don't understand
- newphysist
- · Replies 1 ·
How should I show that lim_n ∫〖f_n dm〗 = ∫〖f dm〗?
- Jack3
- · Replies 1 ·
Compute the integral of the Cantor-Lebesgue function ∫_0^1〖F(x)〗 dm .
- Jack3
- · Replies 1 ·
What is a function that is continuous at all points except the rationals?
- Dustinsfl
- · Replies 5 ·
Continuous Except Jump Discontinuity: Showing True for Any Function
- Dustinsfl
- · Replies 1 ·
Graduate Continuous function from (0,1) onto [0,1]?
- dumbQuestion
- · Replies 4 ·
Graduate Complex analysis integration. Strange result
- McLaren Rulez
- · Replies 6 ·
Graduate Proving monotonicity of a ratio of two sums
- raphile
- · Replies 3 ·
Graduate What is e^-iPi/2 and how can it be represented using cos and sin notation?
- DiracPool
- · Replies 3 ·
Domain of σ(x,y) = Σ 1/((k+x)(k+y)) for non-positive values
- chisigma
- · Replies 2 ·
Undergrad Proofing the derivatives of e^x from the limit approach
- ibelive
- · Replies 19 ·
Graduate Partial derivative exists at origin but not continuous there
- mathFun
- · Replies 4 ·
Undergrad What is the meaning of that a function F is well-defiened ?
- Maths Lover
- · Replies 2 ·
Undergrad How Does the Ratio Test Prove Series Convergence?
- Bipolarity
- · Replies 3 ·
Graduate Conformal Mapping for Transforming Regions: Finding a Function
- MaxJasper
- · Replies 1 ·
Graduate What is [itex]{\delta ^n}(f(x))[/itex] in n dimensions?
- friend
- · Replies 15 ·
Graduate What is the Set Intersection of Successive Midpoint Triangles in R^2?
- rakehsoran
- · Replies 3 ·
Cantor set and ternary expansions without the digit 1
- Dustinsfl
- · Replies 1 ·
Graduate Complex analysis- show that the integral of this function exists
- jrp131191
- · Replies 3 ·
Cantor ternary set, construction
- Dustinsfl
- · Replies 1 ·
Question on proof of completness of space of all complex valued functions
- oblixps
- · Replies 1 ·
Proving sup of tail of one sequence ≤ sup of tail of another
- OhMyMarkov
- · Replies 2 ·
Graduate Finding inverse for a homeomorphism on the sphere (compactification)
- huberscher
- · Replies 13 ·
Graduate Explanation of uniform topology theorem in Munkres
- mathmonkey
- · Replies 3 ·
Graduate The circle as a set closed and bounded
- dapias09
- · Replies 7 ·
Graduate Inverse of Function: Topology by Munkres Ch 1
- trixitium
- · Replies 2 ·
Graduate What is Topological Equivalence in Functions and Dynamical Systems?
- marellasunny
- · Replies 3 ·
Graduate Checking if a function is analytic or entire
- fleazo
- · Replies 1 ·
Graduate Questions on locally compact space
- jtceleron
- · Replies 3 ·
Graduate Can Direct Use of cosh(2y) and cos(2x) Prove the Trigonometric Identity?
- MrWarlock616
- · Replies 4 ·
Undergrad Completeness axiom as having no holes in the set
- Bipolarity
- · Replies 4 ·
Graduate Subspace topology of Rationals on Reals
- dumbQuestion
- · Replies 1 ·
Undergrad Schwarz inequality is Cauchy–Schwarz inequality?
- rfrederic
- · Replies 5 ·
Proving $\lim_{n\to\infty}a_n^2 = a^2$ with Delta-Epsilon
- Dustinsfl
- · Replies 4 ·
Are All Countable Sets Closed?
- OhMyMarkov
- · Replies 5 ·
Undergrad Taylor Series Interval of COnvergence and Differention + Integration of it
- Square1
- · Replies 2 ·
Can we use the fact that $L>1$ to show that the sequence is unbounded?
- OhMyMarkov
- · Replies 11 ·
Proof That $\lim\limits_{n\to\infty}\frac{1}{a^n}=0$ if $a>1$
- Dustinsfl
- · Replies 5 ·
Check my integer or decimal solution
- Uniman
- · Replies 1 ·
Graduate What is the value of the integral of a delta function over a finite interval?
- benjamin_cro
- · Replies 6 ·
Dirichlet Problem on Sphere: Proving Mean Value of f
- Dustinsfl
- · Replies 1 ·
Mean square convergence of Fourier series
- Dustinsfl
- · Replies 1 ·
What Else Can the Poisson Kernel Achieve Beyond the Dirichlet Problem?
- Dustinsfl
- · Replies 1 ·
Does integration give the same area as counting unit squares?
- Poirot1
- · Replies 3 ·
Real Analysis is all about infinity
- Tomp
- · Replies 1 ·
Graduate CR Equations: Real & Imaginary Parts Satisfy Cont. & Diff.
- fleazo
- · Replies 3 ·
Graduate Is the Given Statement a Consequence of Fubini's Theorem?
- Tatianaoo
- · Replies 3 ·
Undergrad Proving the real and imaginary part formulas
- CrazyNeutrino
- · Replies 3 ·
Undergrad Function Notation in Real Numbers: What Does it Mean?
- HasuChObe
- · Replies 3 ·
Graduate How Does the Riemann Integral Affect Lp Space Completeness?
- dumbQuestion
- · Replies 3 ·
Continuous periodic piecewise differentiable
- Dustinsfl
- · Replies 1 ·
Why does the boundary term vanish in Fourier series integration by parts?
- Dustinsfl
- · Replies 1 ·
Graduate Lebesgue outer measure of a set of countably many points is 0 - logic check
- dumbQuestion
- · Replies 9 ·
Graduate Open subset of R written as a countable union of pairwise disjoint open intervals?
- dumbQuestion
- · Replies 3 ·
Schwarz and triangle inequalities for ℓ² sequences
- Dustinsfl
- · Replies 1 ·
Limit Points of Unbounded Interval
- OhMyMarkov
- · Replies 1 ·
Graduate Epsilon proof and recursive sequences
- dustbin
- · Replies 4 ·
How can I prove that the infinite union of certain closed sets is not closed?
- OhMyMarkov
- · Replies 3 ·
Graduate Why Is \left[\frac{1}{2},1\right] a Neighborhood of 1 in \left[0,1\right]?
- funcalys
- · Replies 5 ·
Cauchy-Schwarz for square-summable sequences
- Dustinsfl
- · Replies 8 ·
Solving Abs Converge Issue with Ratio Test
- Dustinsfl
- · Replies 1 ·
The minimal uncountable well-ordered set
- topsquark
- · Replies 1 ·
Bounded Set with Two Limit Points
- OhMyMarkov
- · Replies 3 ·
Graduate Compactness/convergence in Banach spaces
- TaPaKaH
- · Replies 5 ·
Laplace general soln (x-x_0)^2 + (y-y_0)^2\leq R^2
- Dustinsfl
- · Replies 1 ·
Undergrad Undergraduate courses for the study of fractals
- Mathematicize
- · Replies 1 ·
Calculation in proof of Poincare's Lemma
- oblixps
- · Replies 4 ·
Graduate Question on constructing a convergent sequence
- ScroogeMcDuck
- · Replies 1 ·
Graduate Does the Gaussian have complex poles?
- mjordan2nd
- · Replies 2 ·
Graduate Proof of "Every Cauchy Sequence is Bounded
- fderingoz
- · Replies 3 ·
Graduate Uniform Convergence: Intuitive Explanation
- stephenkeiths
- · Replies 2 ·
What is the correct formulation of the problem: $0^{0}$?
- chisigma
- · Replies 3 ·
Graduate Variation of Dirac delta function
- friend
- · Replies 5 ·
Graduate Why does a separable dual space contain functionals of arbitrarily large norm?
- AxiomOfChoice
- · Replies 10 ·
Graduate Is [-∞,a) open or closed on the extended real line?
- Fractal20
- · Replies 4 ·
Graduate Complex Analysis Solutions: Real and Imaginary Parts
- Fabio010
- · Replies 1 ·
Is the Sequence $\{x_n\}$ Defined by $7x_{n+1} = x_n^3 + 6$ Increasing?
- Dustinsfl
- · Replies 3 ·
Graduate How Can I Better Understand Advanced Calculus Proofs?
- NukeEng101
- · Replies 3 ·
Graduate What is the Definition of Closed Sets in Topology?
- kimkibun
- · Replies 4 ·
Graduate Is the upper half-space {x ∈ ℝⁿ: xₙ > 0} open?
- stauros
- · Replies 2 ·
What is the Limit of the Poisson Kernel Prove for $r\to 1$?
- Dustinsfl
- · Replies 10 ·
Proving Steady State Temperature Distribution in a Disk
- Dustinsfl
- · Replies 1 ·
Prove Evenness of Poisson Kernel for Fixed $r$
- Dustinsfl
- · Replies 1 ·
Proof of Positive Values for P(r,θ)
- Dustinsfl
- · Replies 1 ·
Graduate Quotient Topology and Adjunction Space
- sammycaps
- · Replies 5 ·
High School Definition Of The Complement Of A Set
- Bashyboy
- · Replies 2 ·
Can You Separate Real and Imaginary Parts of $\sin^{-1}(e^{i\theta})$?
- Amer
- · Replies 2 ·
Undergrad Analytic Continuation of the Exponential Function
- spaderdabomb
- · Replies 17 ·
Fn converges Uniformly to f, prove that f is continuous
- Amer
- · Replies 7 ·
Is Poisson's Kernel Useful for Computing Sums of Cosine Functions?
- Dustinsfl
- · Replies 2 ·
Graduate Extract Real Part From ln(e^{ix}+i)
- cragar
- · Replies 4 ·
Squared Difference of Two Series: Why?
- Dustinsfl
- · Replies 3 ·
Are Geometric Progressions Always Less Than or Equal to Arithmetic Progressions?
- Dustinsfl
- · Replies 4 ·
Undergrad Decomposing even and odd parts of e^ix
- radiator
- · Replies 6 ·
Graduate Nested sequence intersection theorem proof details
- Artusartos
- · Replies 8 ·
Graduate Why must the supremum of a rational subset be rational?
- drobadur
- · Replies 3 ·
Graduate Contour Integration with Singularities: How Does the Residue Theorem Apply?
- chill_factor
- · Replies 2 ·
Graduate Proving differentiability from the Cauchy-Riemann equations
- kostas230
- · Replies 5 ·
Graduate Regarding Einstein Summation Convention
- clayton26
- · Replies 2 ·