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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High School Can Irrational Numbers Ever Align in a Theoretical Game?
- AplanisTophet
- · Replies 14 ·
Undergrad Understanding metric space definition through concrete examples
- Ricster55
- · Replies 3 ·
Undergrad Why Are Topology Axioms Defined the Way They Are?
- kent davidge
- · Replies 1 ·
The proof of the infinite geometric sum
- cbarker1
- · Replies 1 ·
Help with topology and analysis questions
- Kingkong999
- · Replies 1 ·
Insights Hilbert Spaces And Their Relatives - Operators
- fresh_42
- · Replies 3 ·
Undergrad Intuitive understanding of Euler's identity?
- HuskyLab
- · Replies 6 ·
Why does ker(f) = {0} imply f is injective?
- Math Amateur
- · Replies 3 ·
High School Gram-Schmidt orthonormalization span property in Garling theorem 11.4.1
- Math Amateur
- · Replies 5 ·
Undergrad Can you prove a monotonic Cauchy sequence converges by checking consecutive differences?
- FallenApple
- · Replies 5 ·
Span equality in Gram-Schmidt orthonormalization (Garling 11.4.1)
- Math Amateur
- · Replies 1 ·
Proving the complex polarization formula for inner products
- Math Amateur
- · Replies 2 ·
Undergrad Proving the polarization formula for complex inner products
- Math Amateur
- · Replies 3 ·
Undergrad Is Munkres' topology exercise on product spaces false?
- facenian
- · Replies 2 ·
Undergrad Triangle inequality for standard metric on C^d in Garling 11.1.5
- Math Amateur
- · Replies 9 ·
Undergrad Linear transformation with row vectors in Junghenn chapter 9
- Math Amateur
- · Replies 7 ·
Undergrad Is this definition of second-countable topological spaces correct?
- kent davidge
- · Replies 11 ·
Triangle inequality in standard metric on C^d
- Math Amateur
- · Replies 2 ·
How to Derive the Inequality on Page 36 in the Proof of Lemma 11.3?
- Alone
- · Replies 1 ·
Row vs column vector notation in Junghenn Proposition 9.2.3
- Math Amateur
- · Replies 2 ·
Norm of a Linear Transformation: Proving Homogeneity From Definition - Peter
- Math Amateur
- · Replies 2 ·
Why does scalar multiplication commute with the norm of a linear transformation?
- Math Amateur
- · Replies 5 ·
Derivative vs differential in Junghenn Definition 9.1.3
- Math Amateur
- · Replies 2 ·
Derivative of a Real-Valued Function of Several Variables: Junghenn Defn 9.1.3
- Math Amateur
- · Replies 2 ·
Undergrad Norm of a linear transformation under scalar multiplication
- Math Amateur
- · Replies 3 ·
Undergrad Junghenn Theorem 9.2.1: applying Theorem 9.1.10 to complete proof of linearity
- Math Amateur
- · Replies 2 ·
Undergrad Proving |x_j| ≤ √(Σ|x_j|²) in Duistermaat-Kolk Lemma 1.1.7
- Math Amateur
- · Replies 13 ·
Why are norms needed in some limits but not others in Theorem 9.1.10?
- Math Amateur
- · Replies 4 ·
Undergrad Why norms appear in some lines of Theorem 9.1.10 but not others
- Math Amateur
- · Replies 6 ·
Proving |x_j| ≤ √(Σ|x_i|²) in Duistermaat-Kolk Lemma 1.1.7
- Math Amateur
- · Replies 2 ·
Undergrad Derivative vs differential in multivariable analysis
- Math Amateur
- · Replies 3 ·
How Do Cauchy's Estimates Apply to Analytic Functions Within Unit Discs?
- Deanmark
- · Replies 1 ·
Undergrad How to prove f'(a) exists in ℝⁿ from the derivative definition
- Math Amateur
- · Replies 5 ·
High School Is the Explanation of Compactness in [0,1] and (0,1) Accurate?
- BWV
- · Replies 24 ·
Graduate Homology calculation using Mayer-Vietoris sequence
- PsychonautQQ
- · Replies 2 ·
Hadamard lemma: why φₐ(x)y formula implies f(x) = f(a) + φₐ(x)(x-a)
- Math Amateur
- · Replies 5 ·
Undergrad Inequalities for vector-valued function derivatives in Junghenn 9.1.2
- Math Amateur
- · Replies 8 ·
Show the following sequence as a monotone increasing
- cbarker1
- · Replies 3 ·
Inequalities in Junghenn's proof of proposition 9.1.2 on vector derivatives
- Math Amateur
- · Replies 1 ·
Prove this proposition 2.1.13 in Induction to Real Analysis by Jiri Lebel
- cbarker1
- · Replies 1 ·
Directional derivatives and Jacobian notation in Duistermaat and Kolk
- Math Amateur
- · Replies 3 ·
Undergrad Notation for directional derivatives in Duistermaat and Kolk
- Math Amateur
- · Replies 3 ·
Undergrad Directional derivative notation in Duistermaat and Kolk
- Math Amateur
- · Replies 2 ·
Undergrad Homeomorphisms and ##\mathbb{R}##
- kent davidge
- · Replies 3 ·
Undergrad Proposition 2.3.2: deriving partial derivatives from the differential
- Math Amateur
- · Replies 6 ·
Proving partial derivatives follow from directional derivatives in D&K Prop 2.3.2
- Math Amateur
- · Replies 4 ·
Proving assertion (i) from formula (2.11) in D&K Proposition 2.3.2
- Math Amateur
- · Replies 1 ·
Continuity of φₐ in Duistermaat-Kolk Lemma 2.2.7 (Hadamard)
- Math Amateur
- · Replies 2 ·
Undergrad Proposition 2.2.9 in Duistermaat and Kolk's multivariable analysis
- Math Amateur
- · Replies 4 ·
Undergrad Proposition 2.3.2 in Duistermaat and Kolk's multivariable analysis
- Math Amateur
- · Replies 3 ·
Undergrad Why is the subgroup H not a Lie Group under the Subspace Topology?
- kent davidge
- · Replies 4 ·
Undergrad Dense set equivalent definitions
- HAT
- · Replies 5 ·
Undergrad Differential and derivative in Kantorovitz's definition
- Math Amateur
- · Replies 8 ·
Undergrad Hadamard's lemma and continuity of φₐ at a
- Math Amateur
- · Replies 2 ·
Undergrad Hadamard lemma: from φₐ(x)y formula to f(x) = f(a) + φₐ(x)(x - a)
- Math Amateur
- · Replies 5 ·
Why can't real numbers satisfy this absolute value equation?
- mathdad
- · Replies 3 ·
How does Lemma 1.1.7 (iv) imply Proposition 2.2.9?
- Math Amateur
- · Replies 1 ·
Why is the remainder term zero for linear maps in D&K 2.2.5?
- Math Amateur
- · Replies 2 ·
Undergrad Why is the remainder term zero for linear maps in D&K example 2.2.5?
- Math Amateur
- · Replies 3 ·
Limit of φ₀(h)/‖h‖ in Kantorovitz example 4
- Math Amateur
- · Replies 3 ·
Undergrad Kantorovitz Example 4: limit of φ₀(h)/‖h‖ as h→0
- Math Amateur
- · Replies 3 ·
Kantorovitz's definition of differential for multivariable functions
- Math Amateur
- · Replies 3 ·
Undergrad Differential for Real Valued Functions of Several Variables
- Math Amateur
- · Replies 1 ·
Solving Kantorovitz' Example 3 on Real Valued Functions of Several Variables
- Math Amateur
- · Replies 2 ·
Undergrad Partial derivative definition applied to equation (2.3) in Kantorovitz
- Math Amateur
- · Replies 2 ·
Undergrad Proving f(x + h) - f(x) = Σ[F_j(h_j) - F_j(0)] in Kantorovitz
- Math Amateur
- · Replies 4 ·
Undergrad Turning the square into a circle
- Observeraren
- · Replies 9 ·
How does Lemma 2.2.3 Demonstrate the Uniqueness of the Derivative?
- Math Amateur
- · Replies 5 ·
Differentiability of mappings from R^n to R^p .... .... D&K Defn 2.2.2 ....
- Math Amateur
- · Replies 4 ·
Why call a line through x in direction u an axis
- Math Amateur
- · Replies 2 ·
Graduate Homology groups of R^3 minus a tubular neighborhood of a knot
- PsychonautQQ
- · Replies 3 ·
Proving implication (ii) ⟹ (iii) in Duistermaat-Kolk prop. 2.2.1
- Math Amateur
- · Replies 1 ·
Why are the sets in the D&K proof of Heine-Borel open?
- Math Amateur
- · Replies 11 ·
Why doesn't the boundary prevent (A ∩ U) ∪ (A ∩ V) = A in disconnected sets?
- Math Amateur
- · Replies 1 ·
Undergrad Can Complex Equations Break the Bounds of the Unit Circle?
- ADDA
- · Replies 24 ·
Undergrad Importance of Archimedean Property and Density of Rationals
- Mr Davis 97
- · Replies 3 ·
Show that a sequence is bounded, monotone, using The Convergence Theorem
- cbarker1
- · Replies 1 ·
Why does a point in an open ball imply the complement is open?
- Math Amateur
- · Replies 2 ·
Continuity of Euclidean norm in Duistermaat-Kolk Theorem 1.8.15
- Math Amateur
- · Replies 2 ·
Linear mappings are Lipschitz continuous
- Math Amateur
- · Replies 2 ·
Proving the Euclidean norm is Lipschitz continuous
- Math Amateur
- · Replies 2 ·
Reference request - Measure theory
- Joppy
- · Replies 7 ·
Undergrad Why do we need to use causality arguments in the Landau damping problem?
- TheCanadian
- · Replies 12 ·
Norm bounds for inverses in Duistermaat-Kolk 1.8.12
- Math Amateur
- · Replies 6 ·
Equivalence of all norms on R^n in Duistermaat-Kolk
- Math Amateur
- · Replies 2 ·
Does Lipschitz continuity imply uniform continuity in R^n?
- Math Amateur
- · Replies 3 ·
Why does the supremum of f(K) belong to f(K) in D&K Theorem 1.8.8?
- Math Amateur
- · Replies 2 ·
Closed sets in V: reconciling proposition 1.2.17 with definition 1.2.16
- Math Amateur
- · Replies 2 ·
Prove the Following is True About the Complex Function f(z) = e^1/z
- Deanmark
- · Replies 3 ·
Proving D&K Proposition 1.2.17(i) on open and closed sets in V
- Math Amateur
- · Replies 2 ·
Compactness of closed ball in proper mapping theorem (D&K 1.8.6)
- Math Amateur
- · Replies 2 ·
Existence of convergent sequences in proper mappings (Duistermaat-Kolk 1.8.6)
- Math Amateur
- · Replies 2 ·
Compact sets and closed sets characterization in Duistermaat-Kolk
- Math Amateur
- · Replies 6 ·
Negating unboundedness and proving non-compactness in D&K Theorem 1.8.4
- Math Amateur
- · Replies 2 ·
Why does a Cauchy sequence converge if a subsequence does?
- Math Amateur
- · Replies 4 ·
Does Laczkovich-Sos theorem 5.2 have an equivalent in R^n?
- Math Amateur
- · Replies 1 ·
Theorem 11.15: coordinate-wise convergence in R^n
- Math Amateur
- · Replies 1 ·
Undergrad Equidistance of Points in a Sphere?
- shintashi
- · Replies 5 ·
Bolzano-Weierstrass theorem: supremum argument in D&K 1.6.2
- Math Amateur
- · Replies 1 ·
Orthogonal projection in Duistermaat and Kolk example 1.5.3
- Math Amateur
- · Replies 1 ·