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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How Do You Calculate the Real and Imaginary Parts of \( e^{e^z} \)?
- Deanmark
- · Replies 1 ·
Duistermaat and Kolk Example 1.3.8: proving f(ℝ) = [-1, 1]
- Math Amateur
- · Replies 2 ·
Graduate How can I Prove the following Integral Inequality?
- zarei175
- · Replies 2 ·
Visualizing an "As Discontinuous As Possible" Function
- castor28
- · Replies 12 ·
Graduate How to find the domain of functions of an operator
- SemM
- · Replies 19 ·
Remainder converges uniformly to 0
- mathmari
- · Replies 10 ·
[Complex Analysis] Singularity in product of analytic functions
- ludwig1
- · Replies 1 ·
Undergrad Is there a typo in the formula for dividing complex numbers?
- Drakkith
- · Replies 4 ·
How is the remainder for Taylor polynomials calculated?
- mathmari
- · Replies 10 ·
Graduate Convergence of an Integral Involving Lebesgue Measure and Sine Functions
- pawlo392
- · Replies 10 ·
Proving necessity in D&K Lemma 1.3.3 on limits
- Math Amateur
- · Replies 1 ·
Necessary and sufficient conditions in Duistermaat-Kolk lemma 1.3.3
- Math Amateur
- · Replies 1 ·
Graduate Covariant derivative and 'see-saw rule'
- binbagsss
- · Replies 2 ·
Prove that if g(f(x)) is injective then f is injective
- cbarker1
- · Replies 1 ·
Undergrad What is the Difference Between an Angular Sector and a Circular Sector?
- arlesterc
- · Replies 3 ·
Why does A closure equal complement of interior of complement imply A is closed?
- Math Amateur
- · Replies 2 ·
Why is Lemma 1.2.5 restricted to finite collections of open subsets?
- Math Amateur
- · Replies 2 ·
Undergrad Minimum number of moves from a to b
- BiGyElLoWhAt
- · Replies 6 ·
Can Derivatives Exist at Discontinuities of a Piecewise Function?
- mathmari
- · Replies 40 ·
Graduate Sequence induced by short exact sequence
- PsychonautQQ
- · Replies 3 ·
High School Metric for a sphere in polar coordinates
- Arman777
- · Replies 11 ·
Undergrad If A is an algebra, then its uniform closure is an algebra.
- member 587159
- · Replies 4 ·
Undergrad Describing 3d Manifold Objects as a Hypersurface
- decentMO
- · Replies 3 ·
Undergrad What would it even mean to consider a "half" derivative?
- Ethan Singer
- · Replies 4 ·
Tanh is uniformly continous on R
- mathmari
- · Replies 14 ·
Proving Limits of Exponential Series at Infinity
- mathmari
- · Replies 7 ·
High School Can three 2-spheres nest cyclically inside each other?
- Wendel
- · Replies 8 ·
Orthogonality of vectors in Cauchy-Schwarz proof
- Math Amateur
- · Replies 1 ·
Meaning of x^(k) notation in Duistermaat and Kolk lemma 1.1.7
- Math Amateur
- · Replies 1 ·
Undergrad Ordered lattice of topologies on the 3 point set
- jackferry
- · Replies 1 ·
High School Complex products: perpendicular vectors and rotation effects
- Ventrella
- · Replies 3 ·
Find a function so that the composition is continuous
- mathmari
- · Replies 20 ·
Undergrad Can We Mathematically Define Everyday Objects Like Smartphones?
- Tio Barnabe
- · Replies 21 ·
Show that the function is bounded and strictly increasing
- mathmari
- · Replies 12 ·
Is the Function \( f(x) = \sqrt{4 + x^2} \) Continuous Everywhere?
- mathmari
- · Replies 14 ·
Why does Conway define completeness for discrete metric spaces?
- Math Amateur
- · Replies 4 ·
Evaluate Case of Fresnel Integral
- Deanmark
- · Replies 13 ·
Graduate What Is the Role of the Boundary Operator in p-Chains?
- PsychonautQQ
- · Replies 28 ·
High School How a Klein bottle has a 0 volume?
- parshyaa
- · Replies 16 ·
Undergrad Rational sequence converging to irrational
- Delta2
- · Replies 13 ·
Can we somehow modify the Lagrange form to get a tighter bound? (Curious)
- mathmari
- · Replies 8 ·
Finding the Product of Distinct Roots: A Complex Challenge
- lfdahl
- · Replies 1 ·
Additional solution for polar form of complex number
- TheFallen018
- · Replies 1 ·
Complex Variables - Max Modulus Inequality
- joypav
- · Replies 4 ·
Complex Variables - Solution of a System
- joypav
- · Replies 3 ·
Adjoint operator and orthogonal projection
- mathzero
- · Replies 3 ·
Undergrad Map from space spanned by 2 complex conjugate vars to R^2
- Jamz
- · Replies 5 ·
Undergrad Is simulation considered a type of quantitative analysis?
- Trixie Mattel
- · Replies 7 ·
Complex Variables - Zeros of Analytic Functions
- joypav
- · Replies 4 ·
Complex Variables - Legendre Polynomial
- joypav
- · Replies 2 ·
Graduate Torus 2-sheet covering of Klein bottle
- PsychonautQQ
- · Replies 22 ·
High School Is the trefoil knot truly unknottable or is there a way to simplify it?
- DaveC426913
- · Replies 13 ·
Reconciling Differences in Vector-Valued Function Derivatives
- Math Amateur
- · Replies 2 ·
Graduate Transfinite Taylor series of exp(x) and of h(x)
- H Tomasz Grzybowski
- · Replies 6 ·
Where Can I Find a Solution to Zeidler's Eigenvalue Problem?
- Alone
- · Replies 7 ·
Graduate Why Does the Orbit Space of a Covering Map Not Necessarily Equal the Base Space?
- PsychonautQQ
- · Replies 1 ·
Undergrad Cardinality of fibers same for covering maps
- PsychonautQQ
- · Replies 17 ·
Undergrad Choosing points from a set that produce the largest polygon
- Jeff.Nevington
- · Replies 5 ·
High School Square root of a negative number in a complex field
- Adgorn
- · Replies 45 ·
Graduate Fundamental group of a sphere with 6 points removed
- PsychonautQQ
- · Replies 15 ·
Directional derivative in scalar fields vs vector fields
- Math Amateur
- · Replies 2 ·
How Does Definition 8.9 Imply Differentiability Near Point p?
- Math Amateur
- · Replies 1 ·
Proving Browder's proposition 8.12 on vector valued functions
- Math Amateur
- · Replies 1 ·
Graduate 8.12 in Browder's "Mathematical Analysis: An Introduction"
- Math Amateur
- · Replies 4 ·
Does the Sequence Converge?
- evinda
- · Replies 9 ·
Why Does Lemma 8.4 Equal This Expression?
- Math Amateur
- · Replies 5 ·
Why Does Theorem 1.9 Use f(t) Instead of f(γ(t))?
- Math Amateur
- · Replies 2 ·
Graduate Connected sum of manifolds and free group isomorphisms
- PsychonautQQ
- · Replies 15 ·
Why must φ be non-decreasing for γ ∘ φ to preserve trace?
- Math Amateur
- · Replies 1 ·
Undergrad Why can we define sequences in this fashion?
- Oats
- · Replies 2 ·
Insights The Different Faces Of The Special Unitary Group ##SU(2)##
- fresh_42
- · Replies 3 ·
A complex numbers' modulus identity.
- Alone
- · Replies 1 ·
Understanding Cantor's Theorem and Diameter
- Math Amateur
- · Replies 3 ·
Complex Valued Functions BV: John B. Conway Prop 1.3 Explained
- Math Amateur
- · Replies 3 ·
Why is sin u ≥ 2u/π for 0 ≤ u ≤ π/2?
- Math Amateur
- · Replies 4 ·
Graduate Questions about Covering maps, manifolds, compactness
- PsychonautQQ
- · Replies 1 ·
Understand Proposition 1.3 in Conway's Functions of Complex Variables I
- Math Amateur
- · Replies 1 ·
Why is Re(z) ≤ |z| in Palka's Lemma 2.1(vi) proof?
- Math Amateur
- · Replies 2 ·
Palka lemma 2.1(vi): argument of contour integral and modulus property
- Math Amateur
- · Replies 2 ·
How Can \dot{\gamma}(0) Fail to Exist in Palka's Example 1.3?
- Math Amateur
- · Replies 2 ·
Undergrad Where can I find a proof of the Swiss cheese theorem?
- Bestfrog
- · Replies 5 ·
Deriving the simplified expression in Conway's Theorem 2.29
- Math Amateur
- · Replies 2 ·
Insights Representations Of The Special Unitary Group SU(2)
- fresh_42
- · Replies 3 ·
Complex number geometrical problem
- amr21
- · Replies 4 ·
Mapping of a Circle in the Complex Plane
- amr21
- · Replies 7 ·
Proof of Divergence: (-1)^n Sequence
- solakis1
- · Replies 8 ·
Do we distinguish cases for n?
- evinda
- · Replies 12 ·
Analyticity of √(1 + z²) and branch point exclusion in Palka Ch. III
- Math Amateur
- · Replies 2 ·
High School Why does √(-i²) give two different answers?
- Tian En
- · Replies 6 ·
How Can We Prove the Modified Bernoulli Inequality?
- evinda
- · Replies 6 ·
Graduate Fundamental group of n connect tori with one point removed
- PsychonautQQ
- · Replies 9 ·
Undergrad Intuition behind induced homomorphism from covering maps
- PsychonautQQ
- · Replies 15 ·
Graduate Fundamental group of Project Plane with 2 points missing
- PsychonautQQ
- · Replies 6 ·
Lemma 3.1 on disconnected sets in Palka's complex analysis
- Math Amateur
- · Replies 2 ·
Limit of e^(-1/z^2) in Palka section 2.2
- Math Amateur
- · Replies 2 ·
Palka's limit of complex function with logarithm
- Math Amateur
- · Replies 2 ·
Continuity of the argument function in complex plane topology
- Math Amateur
- · Replies 2 ·
Undergrad Impossible to lift the identity map on the circle
- PsychonautQQ
- · Replies 3 ·
Undergrad Why does the boundary matter for compactness in R²?
- FallenApple
- · Replies 12 ·
Undergrad Retract of a connected space is connected
- PsychonautQQ
- · Replies 6 ·