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.
Sub-forums
Threads
Undergrad Proof that retract of Hausdorff space is closed
- PsychonautQQ
- · Replies 1 ·
Undergrad How Does Closure in a Neighborhood Imply Membership in a Set?
- PsychonautQQ
- · Replies 12 ·
The Residue Theorem To Evaluate Integrals
- joypav
- · Replies 5 ·
Undergrad Is S^2 - {N} Homeomorphic to R^2?
- PsychonautQQ
- · Replies 3 ·
Using Residue Theorem To Prove Value Of Summation
- joypav
- · Replies 4 ·
Undergrad Euler Characteristic of the Projective plane and sphere?
- PsychonautQQ
- · Replies 3 ·
Undergrad What is an atlas for a torus manifold?
- aheight
- · Replies 4 ·
Theorem 1.8: Sets or Domains in the Complex Plane - Palka Ch.2
- Math Amateur
- · Replies 3 ·
Why Does γ(t) = z(1-t) Represent the Same Curve in Reverse?
- Math Amateur
- · Replies 1 ·
Undergrad Homotopy Class vs Fundamental Group.
- FallenApple
- · Replies 6 ·
Graduate Is the Long Line Locally Euclidean, Hausdorff, and Path Connected?
- PsychonautQQ
- · Replies 3 ·
Limit notation in Bartle and Sherbert Theorem 7.3.5
- Math Amateur
- · Replies 2 ·
Proof of Bartle and Sherbert Theorem 7.3.5 on the Riemann integral
- Math Amateur
- · Replies 2 ·
Convergence in topological space
- Julio1
- · Replies 2 ·
Riemann Integration - The Additivity Theorem .... B&S Theorem 7.2.9 ....
- Math Amateur
- · Replies 1 ·
Limit superior theorem 3.4.11 proof in Bartle and Sherbert
- Math Amateur
- · Replies 5 ·
Undergrad Proving Convergence: Solving the Limit of 1/(6n^2+1) = 0
- Mr Davis 97
- · Replies 8 ·
Undergrad How can we characterize mathematical analysis?
- Mr Davis 97
- · Replies 2 ·
Undergrad How Does the Supremum of -A Relate to Its Elements?
- Mr Davis 97
- · Replies 5 ·
Density theorem application to subsequential limits of rationals
- Math Amateur
- · Replies 2 ·
Graduate Hahn-Banach From Systems of Linear Equations
- bolbteppa
- · Replies 9 ·
High School Complex numbers imaginary part
- MikeSv
- · Replies 11 ·
Undergrad Proving that square root of 2 exists
- Mr Davis 97
- · Replies 16 ·
Undergrad Proving every irreducible representation of SU(2) uses ladder operators
- davidge
- · Replies 3 ·
Undergrad Noncompact locally compact Hausdorff continuous mapping
- PsychonautQQ
- · Replies 14 ·
Undergrad Continuity of the determinant function
- dextercioby
- · Replies 1 ·
Undergrad Can a Topological Space be Both a 1-Manifold and an n-Manifold?
- PsychonautQQ
- · Replies 17 ·
Undergrad Generalization of measure theory to uncountable unions
- greypilgrim
- · Replies 5 ·
L'Hospital's Rule proof in Bartle and Sherbert Theorem 6.3.3
- Math Amateur
- · Replies 3 ·
Undergrad Conjugate of αe^(iα) when α is complex
- dyn
- · Replies 20 ·
Why does sin x / √x equal cos x / (1/2√x)?
- Math Amateur
- · Replies 2 ·
Proving Corollary 6.2.2 of Bartle and Sherbert Theorem 6.2.1
- Math Amateur
- · Replies 8 ·
Undergrad Interior Extremum Theorem corollary proof and continuity assumption
- Math Amateur
- · Replies 3 ·
Undergrad Is e: [0,1] --> S^1 a Quotient Map?
- PsychonautQQ
- · Replies 3 ·
Undergrad Does L_g pass to the quotient G/H?
- PsychonautQQ
- · Replies 4 ·
Undergrad What Is a Non-Linear Ordered Set?
- Silviu
- · Replies 1 ·
Undergrad Is R_d x R Locally Euclidean of Dimension 1?
- PsychonautQQ
- · Replies 1 ·
Caratheodory's theorem in B&S chain rule proof
- Math Amateur
- · Replies 3 ·
Undergrad Gluing lemma / infinite corollary
- PsychonautQQ
- · Replies 6 ·
Undergrad Contort rectangle to torus minus splice=homomorphism?
- aheight
- · Replies 1 ·
Undergrad Why is this line not homeomorphic to the unit circle?
- Mr Davis 97
- · Replies 10 ·
Undergrad Proving |x| < |p| + 1 from |x - p| < 1
- Math Amateur
- · Replies 2 ·
Show that there are points Q,R on C such that the triangle PQR is equilateral.
- lfdahl
- · Replies 1 ·
Lipschitz Condition and Uniform Continuity
- Math Amateur
- · Replies 1 ·
Undergrad Relation of completeness to the l.u.b. property?
- Mr Davis 97
- · Replies 5 ·
Why is f continuous at x in Bartle-Sherbert theorem 5.3.2?
- Math Amateur
- · Replies 2 ·
Undergrad Square root of a complex number
- Nipon Waiyaworn
- · Replies 5 ·
Finite rationals with denominator less than n₀
- Math Amateur
- · Replies 2 ·
Proving the Sum of a Sequence Equals n Using Induction
- joypav
- · Replies 6 ·
Undergrad Pole in Stereographic Projection
- FallenApple
- · Replies 1 ·
Graduate Algebraic topology applied to Neuroscience
- Auto-Didact
- · Replies 2 ·
Why |x - 2| < 1/2 implies |x - 1| > 1/2
- Math Amateur
- · Replies 3 ·
Bartle and Sherbert theorem 4.2.9: why f(x) > L/2 > 0?
- Math Amateur
- · Replies 2 ·
High School Understanding Extremum and Derivatives at Boundary Points
- Leo Authersh
- · Replies 4 ·
High School Why does |ψ|² give different results for fe^ikx + ge^ikx?
- Isaac0427
- · Replies 3 ·
High School Graphical Representation of a Complex Sphere
- Leo Authersh
- · Replies 6 ·
Undergrad Simplicial complex geometric realization 1-manifold
- PsychonautQQ
- · Replies 2 ·
Proving |x| < |p| + 1 from |x - p| < 1
- Math Amateur
- · Replies 3 ·
High School Does Every Set in the Axiom of Choice Include an Empty Set?
- kidsasd987
- · Replies 1 ·
Proving z_n > 1 and z_(n+1) < z_n for z_n = c^(1/n)
- Math Amateur
- · Replies 6 ·
Limits of Sequences .... Stoll Theorem 2.2.6
- Math Amateur
- · Replies 4 ·
Ordering on the Set of Real Numbers .... Sohrab, Exercise 2.1.10 (1) ....
- Math Amateur
- · Replies 2 ·
Sohrab exercise 2.1.12 part 1 on ordering of real numbers
- Math Amateur
- · Replies 2 ·
Sohrab exercise 2.1.10(b): ordering on real numbers
- Math Amateur
- · Replies 5 ·
Sohrab Exercise 2.1.10 (c): ordering on real numbers
- Math Amateur
- · Replies 3 ·
Undergrad Show that c^(1/n) is decreasing and greater than 1
- Math Amateur
- · Replies 3 ·
Undergrad What does "zero to order" mean in analysis?
- Tomtam
- · Replies 4 ·
Undergrad Ascending subset sequence with axiom of choice
- jostpuur
- · Replies 3 ·
Open Sets - Unions and Intersections -
- Math Amateur
- · Replies 8 ·
Proving lim(1/(1+na))=0 using epsilon-delta definition
- Math Amateur
- · Replies 3 ·
How to use DeMoivre's theorem to find the product of complex numbers?
- karush
- · Replies 13 ·
Union of intervals [1/n, 1-1/n] equals (0,1) in Sohrab 2.2.4
- Math Amateur
- · Replies 3 ·
Proving ℕ and ℤ are closed sets in ℝ
- Math Amateur
- · Replies 2 ·
Undergrad Can a Circular Function with Complex Variable Represent a 3D Graph?
- Leo Authersh
- · Replies 7 ·
Hcc8.11 change each to complex form and find product
- karush
- · Replies 3 ·
Nested intervals theorem proof in Sohrab theorem 2.1.45
- Math Amateur
- · Replies 2 ·
Theorem 2.1.45: supremum property and nested intervals
- Math Amateur
- · Replies 2 ·
Theorem 2.1.45: supremum property and nested intervals theorem in Sohrab
- Math Amateur
- · Replies 2 ·
Undergrad Hyperreal Convergence: Is It 0 or Infinitesimal?
- Someone2841
- · Replies 1 ·
Undergrad Nested intervals uniqueness proof in Sohrab theorem 2.1.45
- Math Amateur
- · Replies 3 ·
Undergrad Can Complex Numbers Be Viewed as Real Numbers on the X and Y Plane?
- Leo Authersh
- · Replies 5 ·
Undergrad Why Does the Cut of $\mathbb{Q}$ Correspond to $\sqrt{2}$?
- Mr Davis 97
- · Replies 3 ·
Undergrad Supremum Property, Archimedean Property, Nested Intervals
- Math Amateur
- · Replies 4 ·
Undergrad Sohrab theorem 2.1.45: nested intervals and kₙ₊₁ logic
- Math Amateur
- · Replies 2 ·
Undergrad Branch cuts for F(it)-F(-it) where F(z)=√(z²+A²)
- JasonPhysicist
- · Replies 1 ·
Sohrab Exercise 2.1.29 on equivalence of supremum and infimum properties
- Math Amateur
- · Replies 6 ·
Corollary 2.1.39 and Exercise 2.1.40 in Sohrab's Basic Real Analysis
- Math Amateur
- · Replies 4 ·
Why can we assume x > 0 in Sohrab's density of Q in R proof?
- Math Amateur
- · Replies 2 ·
AM-GM inequality proof using strong induction in Sohrab 2.1.25
- Math Amateur
- · Replies 3 ·
Undergrad Sohrab's proof of AM-GM inequality using induction
- Math Amateur
- · Replies 2 ·
Cauchy's inequality: using the discriminant method from Sohrab 2.1.23
- Math Amateur
- · Replies 2 ·
Undergrad Can a tetrahedron have all dihedral angles rational?
- Zafa Pi
- · Replies 4 ·
Undergrad Differentiating a particular integral (retarded potential)
- DavideGenoa
- · Replies 2 ·
Undergrad Bloch theorem 1.4.6: why S ⊆ ℕ from the definition
- Math Amateur
- · Replies 7 ·
High School Symmetric Hamiltonian cycle on tesseract graph in 4D
- DaveC426913
- · Replies 3 ·
Bloch Theorem 1.4.6: why does S ⊆ ℕ from the definition of ℕ
- Math Amateur
- · Replies 4 ·
Bloch Exercise 1.5.9 (3): proving k exists for (r + 1/k)² < s
- Math Amateur
- · Replies 2 ·
Proving the sum of a rational and irrational number is irrational
- Math Amateur
- · Replies 3 ·
Peano Postulate (a) and why p ≠ 1 in theorem 1.3.7
- Math Amateur
- · Replies 3 ·
Undergrad Difference between homeomorphisms, homotopies and deformation retracts
- Silviu
- · Replies 13 ·