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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Graduate Ramanujan Summation and ways to sum ordinarily divergent series
- bhobba
- · Replies 41 ·
Operator norm supremum inequality in Field's theorem 9.2.9
- Math Amateur
- · Replies 2 ·
High School Introductory topology question after real analysis
- Eclair_de_XII
- · Replies 22 ·
Operator norm: why sup and inf are actually max and min in Browder Lemma 8.4
- Math Amateur
- · Replies 2 ·
Operator Norm for Linear Transformations: Browder Ch. 8, Section 8.1, Page 179
- Math Amateur
- · Replies 5 ·
Operator norm definitions in Browder vs Field
- Math Amateur
- · Replies 2 ·
Undergrad Embedding homeomorphic manifolds
- Q-1
- · Replies 42 ·
The metrices are topologically but not strongly equivalent
- mathmari
- · Replies 10 ·
The Elusive Field Structure of $\mathbb{R}^n$ Beyond $n=2$
- Math Amateur
- · Replies 3 ·
How do I solve for a_3 in a complex Fourier series?
- Tan Thom
- · Replies 2 ·
Are the Metrics \(d_1\), \(d_2\), and \(d_{\infty}\) Strongly Equivalent?
- mathmari
- · Replies 4 ·
Is the relation between limit points and closed sets clear? (Wondering)
- mathmari
- · Replies 8 ·
Undergrad How Does Vector Subtraction Relate to Topology?
- doggydan42
- · Replies 19 ·
Proving arcsin x is continuous on [-1, 1]
- Math Amateur
- · Replies 3 ·
Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III
- Math Amateur
- · Replies 2 ·
Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III
- Math Amateur
- · Replies 2 ·
Where Does the Sign of n Matter in Palka's Examples?
- Math Amateur
- · Replies 2 ·
How is Equation (1) Equivalent to the Derivative Definition in Theorem 7.1?
- Math Amateur
- · Replies 4 ·
Graduate DFT k values and their dependence on interval length
- SchroedingersLion
- · Replies 4 ·
Undergrad How to derive the Fourier transform of a comb function
- arcTomato
- · Replies 4 ·
Undergrad Is a limit point compact subspace of a Hausdorff space necessarily closed?
- facenian
- · Replies 8 ·
Undergrad Complex Fourier transform (represented by Σ)
- arcTomato
- · Replies 4 ·
Undergrad How do charts on differentiable manifolds have derivatives without a metric?
- jackferry
- · Replies 20 ·
Graduate Fourier transform and derivation
- arcTomato
- · Replies 7 ·
Undergrad Differentiable manifolds over fields other than R, C
- WWGD
- · Replies 13 ·
Verify Gamelin's Remark: Complex Square and Square Root Functions
- Math Amateur
- · Replies 3 ·
Show that there is no order relation on K
- mathmari
- · Replies 9 ·
Show that there exists a bijection
- mathmari
- · Replies 8 ·
Proving two functions are one-to-one and choosing the correct inverse formula
- AutGuy98
- · Replies 2 ·
Undergrad Discrete Topology and Closed Sets
- joshthekid
- · Replies 12 ·
Undergrad What is wrong with this proof? (divergence of the harmonic series)
- BWV
- · Replies 6 ·
Complex function with derivative only at zero
- Math Amateur
- · Replies 2 ·
Proof of an Infimum Being Equal to the Negative Form of a Supremum ()
- AutGuy98
- · Replies 2 ·
Undergrad Trouble with infinity and complex numbers
- Troxx
- · Replies 12 ·
High School Why is equation (4.26) a quadratic form identity?
- Heidi
- · Replies 6 ·
Understanding Differentiability and Continuity in Complex Analysis
- Math Amateur
- · Replies 2 ·
Lim sup inequality in Denlinger theorem 2.9.6(b)
- Math Amateur
- · Replies 4 ·
Denlinger theorem 2.9.6 (a): upper and lower limit inequality
- Math Amateur
- · Replies 2 ·
Proof of upper and lower limits in Sohrab 2.2.39(a)
- Math Amateur
- · Replies 6 ·
Undergrad Assigning a value for integrating a divergent oscillatory function to infinity
- Swamp Thing
- · Replies 8 ·
Proving Sohrab's proposition 2.2.39 (b) on lim sup and lim inf
- Math Amateur
- · Replies 2 ·
How Does Theorem 4.29 Illustrate Continuity Issues in Inverse Functions?
- Math Amateur
- · Replies 2 ·
Undergrad Different metrics in different dimensions
- Bob3141592
- · Replies 2 ·
Open covering in Apostol's Theorem 4.25 proof
- Math Amateur
- · Replies 2 ·
Applying triangle inequality in Zill & Shanahan theorem 3.1.1
- Math Amateur
- · Replies 3 ·
Convergence of coordinate sequences in R^n
- Math Amateur
- · Replies 6 ·
Graduate How Does the Chain Rule Apply to Pushforwards in Differential Geometry?
- sanad
- · Replies 7 ·
Carothers' Definitions: Neighborhoods, Open Sets, and Open Balls
- Math Amateur
- · Replies 2 ·
Why does the discrete metric generate the power set topology?
- Math Amateur
- · Replies 2 ·
Carothers exercise 32: open balls in normed vector spaces
- Math Amateur
- · Replies 4 ·
Undergrad Division of a complex number by zero
- dyn
- · Replies 7 ·
Why closure points are characterized by open neighborhoods in Browder 6.8
- Math Amateur
- · Replies 3 ·
Baire Category Theorem .... Stromberg, Theorem 3.55 .... ....
- Math Amateur
- · Replies 7 ·
Graduate Baire Category Theorem proof in Stromberg 3.55
- Math Amateur
- · Replies 5 ·
Why is bdry E empty iff E is both open and closed?
- Math Amateur
- · Replies 2 ·
Graduate Fourier Series = Re(Power Series)
- joeblow
- · Replies 3 ·
Why is \( c'' \) an Upper Bound for \( U \cap [a, b] \) in Theorem 3.47?
- Math Amateur
- · Replies 2 ·
Why does density of A in X let us select x ∈ A with ρ(x, z) < ε/2?
- Math Amateur
- · Replies 2 ·
Graduate General formula for lenses without spherical abberation
- mfb
- · Replies 3 ·
Maximum Likelihood Estimation Formula Simplification and Solution for p?
- SheepLon
- · Replies 5 ·
Stromberg Lemma 3.44: why B_ε(x) ∩ A ⊃ B_{1/n}(x) ∩ A_{1/n}
- Math Amateur
- · Replies 2 ·
Heine-Borel theorem: why does compactness imply boundedness in Stromberg 3.40
- Math Amateur
- · Replies 2 ·
Proving U ⊂ S' in Stromberg's theorem 3.36
- Math Amateur
- · Replies 5 ·
Proving a limit to infinity using epsilon-delta
- brooklysuse
- · Replies 3 ·
Verifying that a collection of open intervals covers [a,b] in Stromberg Example 3.34(c)
- Math Amateur
- · Replies 2 ·
Why does Br(a) ⊂ Uj for all j when r = min{r1,...,rn}?
- Math Amateur
- · Replies 3 ·
Finding Cluster Points/Accumulation Points
- brooklysuse
- · Replies 2 ·
Why is the Series Absolutely Convergent for Sequences in l^2(N)?
- Math Amateur
- · Replies 2 ·
Undergrad Theorem 4.3.4 in Sohrab: why f⁻¹(O') = S ∩ O
- Math Amateur
- · Replies 3 ·
Heine-Borel Theorem .... Sohrab, Theorem 4.1.10 .... ....
- Math Amateur
- · Replies 2 ·
Sohrab Proposition 4.1.9: choosing d in proof that closed bounded intervals are compact
- Math Amateur
- · Replies 3 ·
Undergrad Proving an open cover has no finite subcover in Sohrab 4.1.8
- Math Amateur
- · Replies 3 ·
Why the open cover in Sohrab's Proposition 4.1.8 has no finite subcover
- Math Amateur
- · Replies 2 ·
Graduate Fractional Calculus and Residues
- Harrisonized
- · Replies 2 ·
Sohrab Proposition 4.1.1: Lindelof property proof details
- Math Amateur
- · Replies 4 ·
Undergrad Compact Subsets of R .... Sohrab, Proposition 4.1.1 (Lindelof) ....
- Math Amateur
- · Replies 8 ·
Graduate Functional differentiability: Frechet, but not Hadamard?
- Testguy
- · Replies 1 ·
Graduate A question about the proof of the simple approximation lemma
- Artusartos
- · Replies 1 ·
Lindelof covering theorem: countable subcover from uncountable set
- Math Amateur
- · Replies 2 ·
Undergrad Lindelof covering theorem: countable subcollection from uncountable set
- Math Amateur
- · Replies 2 ·
Graduate Mapping of algebraic function to Riemann surface?
- jackmell
- · Replies 1 ·
Graduate CW complex for infinite holed torus? (Surface of infinite genus)
- dumbQuestion
- · Replies 1 ·
Graduate Topology: Munkres - Urysohn lemma
- Fisicks
- · Replies 1 ·
Graduate Identifying Compact Sets in the Slitted and Moore Planes: What's the Method?
- ForMyThunder
- · Replies 1 ·
Graduate Does SU(2) Commutativity Conflict with Its Non-Euclidean Structure?
- Kontilera
- · Replies 1 ·
Graduate Is the Integral Inequality Possible to Prove for Certain Parameters?
- amirmath
- · Replies 1 ·
Graduate Inquiry: Wavelet factorisation / Daubechies method /
- MednataMiza
- · Replies 1 ·
Graduate Two definitions of locally compact
- Fredrik
- · Replies 1 ·
Graduate How to Estimate the Operator Norm ||A||_2 for a Difference Operator?
- Max Fleiss
- · Replies 1 ·
Sohrab Proposition 2.3.15 on e: inequality with lim inf
- Math Amateur
- · Replies 2 ·
Sohrab Proposition 2.3.15: why does t_n ≤ s_n imply lim sup(t_n) ≤ e
- Math Amateur
- · Replies 4 ·
Proposition 2.3.15: Understanding Sohrab's Basic Real Analysis Proof
- Math Amateur
- · Replies 2 ·
Undergrad Sohrab Proposition 2.3.15: why does t_n ≤ s_n imply lim sup(t_n) ≤ e
- Math Amateur
- · Replies 2 ·
Graduate Proof of the L'Hôpital Rule for the Indeterminate Form
- 3.1415926535
- · Replies 2 ·
Proving Sohrab Theorem 2.3.9(a) comparison test using Theorem 2.3.6
- Math Amateur
- · Replies 2 ·
Graduate What does equilibrium mean in portfolio choice and asset pricing?
- woundedtiger4
- · Replies 1 ·
Graduate The correct domain of self-adjointness for the Laplacian
- AxiomOfChoice
- · Replies 1 ·
Graduate How to generalize Newtonian and Lagrangian mechanics
- jostpuur
- · Replies 1 ·
Convergence of Sohrab Exercise 2.3.10 (1)
- Math Amateur
- · Replies 2 ·
Graduate Residue Proof of Fourier's Theorem Dirichlet Conditions
- bolbteppa
- · Replies 1 ·