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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Proving the limit of Lp norms ratio equals infinity norm
- joypav
- · Replies 1 ·
Undergrad How to confirm the function has genus 116?
- aheight
- · Replies 3 ·
Undergrad Completeness of a basis function
- member 428835
- · Replies 32 ·
Undergrad Iterating powers of complex integers along axes of symmetry
- Ventrella
- · Replies 3 ·
Undergrad Do partial derivatives commute in general?
- jk22
- · Replies 5 ·
Graduate Derive Birkhoff Ergodic Theorem from Von Neumann
- wrobel
- · Replies 1 ·
Graduate Structure preserved by strong equivalence of metrics?
- lugita15
- · Replies 2 ·
Graduate Same open sets + same bounded sets => same Cauchy sequences?
- lugita15
- · Replies 2 ·
Hubbard and Hubbard equation 1.7.10: limit sign change as h approaches 0
- Math Amateur
- · Replies 1 ·
Finding border points and then interior points
- A.Magnus
- · Replies 1 ·
Undergrad Trying to understand why a set is both open and closed
- Mr Davis 97
- · Replies 7 ·
Find the square roots of 4*sqrt(3)+4(i)
- Elissa89
- · Replies 3 ·
Undergrad Existence of Directional Derivative in Normed Linear Space
- Gear300
- · Replies 12 ·
Convex Functions: Find $f,g$ Satisfying f(x)=g(x) iff x is an Integer
- evinda
- · Replies 9 ·
Undergrad Topology Words: Reasons for the particular names
- Cantor080
- · Replies 2 ·
Proving Convexity of $f: \mathbb{R} \to \mathbb{R}$
- evinda
- · Replies 1 ·
Scalar projection vs norm of vector projection in Lovric's Theorem 1.6
- Math Amateur
- · Replies 2 ·
Undergrad Open balls contained in other open balls
- Mr Davis 97
- · Replies 11 ·
Undergrad Why does f(x)=x (x≤0) or 1+x (x>0) map open sets to open sets?
- Robin04
- · Replies 9 ·
Undergrad Using the Baire Category theorem
- Mr Davis 97
- · Replies 2 ·
Does the Series Sum of Differences Converge Given a Contractive Condition?
- evinda
- · Replies 1 ·
Proving Convergence of a Sequence with a Geometric Condition
- evinda
- · Replies 3 ·
Finding the Limit Inferior and Limit Superior of a Sequence
- evinda
- · Replies 6 ·
Show existence of subsequences
- evinda
- · Replies 4 ·
Sequence has convergent subsequence
- evinda
- · Replies 2 ·
Tu's theorem 2.2: tangent vectors as derivations at a point
- Math Amateur
- · Replies 2 ·
Why are smooth functions R^n → R used to define tangent vectors as derivations?
- Math Amateur
- · Replies 2 ·
Why Can't Two Functions Cover the Unit Circle?
- Math Amateur
- · Replies 2 ·
Lusin's Theorem - Infinite Measure and not Real-Valued Extensions
- joypav
- · Replies 1 ·
Taylor's Theorem .... Loring W. Tu, Lemma 1.4 .... ....
- Math Amateur
- · Replies 2 ·
What does vol₂ mean in Hubbard's geometric interpretation of k-forms?
- Math Amateur
- · Replies 2 ·
Metric spaces and normed spaces
- ozkan12
- · Replies 4 ·
Dot product projection in Bachman's 1-forms section
- Math Amateur
- · Replies 2 ·
Understanding Lusin's Theorem for $\mathbb{R}$ and Its Proof
- joypav
- · Replies 1 ·
How does ||a + t(a/||a||)|| = (||a|| - t)?
- Math Amateur
- · Replies 3 ·
Abbott's theorem 6.5.1: why power series converges on R or bounded interval
- Math Amateur
- · Replies 2 ·
Pointwise limit of x^(1/(2n-1)) in Abbott example 6.2.2
- Math Amateur
- · Replies 4 ·
Evaluating i^(-21/2)
- Asawira Emaan
- · Replies 6 ·
Graduate Analytical function from numerable point set
- hilbert2
- · Replies 6 ·
Ap1.3.51 are complex numbers, show that
- karush
- · Replies 4 ·
Undergrad Is every metric space homeomorphism an isometry?
- facenian
- · Replies 15 ·
Undergrad Can we have a pasting lemma for uniform continuous functions
- PKSharma
- · Replies 2 ·
Undergrad Hausdorff Metric: Definition 1 vs. Definition 2
- Mr Davis 97
- · Replies 1 ·
Measure Theory - Existence of Fsigma set contained in measurable set
- joypav
- · Replies 1 ·
Are Injective R-Linear Mappings in C Necessarily Surjective?
- Math Amateur
- · Replies 1 ·
Law of cosines for complex numbers in Remmert section 1.3
- Math Amateur
- · Replies 1 ·
How does Remmert derive the Cauchy-Schwarz Inequality in complex functions?
- Math Amateur
- · Replies 4 ·
Undergrad Flipping the sign in the definition of derivative
- Mr Davis 97
- · Replies 3 ·
Undergrad Result regarding signs and a limit
- Mr Davis 97
- · Replies 3 ·
Undergrad R-linear and C-linear mappings of C into C in Remmert
- Math Amateur
- · Replies 4 ·
R-linear and C-linear mappings of ℂ into ℂ
- Math Amateur
- · Replies 3 ·
High School Spivak's Calculus as a Prerequisite for General Topology
- CaptainAmerica17
- · Replies 25 ·
Undergrad Complex differentiability implies real differentiability and C-linear differentials
- Math Amateur
- · Replies 4 ·
Graduate Does dim(M_α)=p when α is a wedge product of p vectors?
- kiuhnm
- · Replies 7 ·
Complex and real differentiability in Remmert's theory of complex functions
- Math Amateur
- · Replies 1 ·
Why is ln(k) a Complex Number When k is a Positive Integer?
- highmath
- · Replies 1 ·
Graduate Is There a Unique Hodge Star Operator for Any p-Vector in Differential Forms?
- kiuhnm
- · Replies 2 ·
Is e^x a transcendental function?
- highmath
- · Replies 5 ·
Undergrad The Chain Rule for Multivariable Vector-Valued Functions ....
- Math Amateur
- · Replies 5 ·
Chain rule theorem 12.7 proof in Apostol's Mathematical Analysis
- Math Amateur
- · Replies 2 ·
Lafontaine's vector form of the differential definition
- Math Amateur
- · Replies 4 ·
Undergrad Metric Spaces and Topology in Analysis
- Mr Davis 97
- · Replies 1 ·
Why is a multi-valued function considered a function?
- highmath
- · Replies 1 ·
Graduate Show that set is an orthonormal set in PC(0,l)
- Shackleford
- · Replies 4 ·
Equivalence of Shifrin's and Lafontaine's definitions of differentiability
- Math Amateur
- · Replies 4 ·
Why directional derivatives can exist without continuity while total derivatives imply it
- Math Amateur
- · Replies 3 ·
Directional derivative formula in Apostol 12.2 Example 4
- Math Amateur
- · Replies 2 ·
Undergrad How to prove that compact regions in surfaces are closed?
- Gene Naden
- · Replies 12 ·
Properties of Functions of Bounded Variation
- joypav
- · Replies 3 ·
Bounded Variation - Difference of Functions
- joypav
- · Replies 5 ·
Proof of the norm inequality in Apostol's theorem
- Math Amateur
- · Replies 4 ·
Using Rolle's theorem to prove for roots (part 2)
- Joe20
- · Replies 2 ·
Undergrad Confused by the behavior of sqrt(z^2+1)
- Measle
- · Replies 6 ·
Using Rolle's theorem to prove for roots
- Joe20
- · Replies 2 ·
Continuous and differentiability
- Joe20
- · Replies 1 ·
Is the limit of the sequence $\left(1+\frac{1}{\sqrt{n}}\right)^n$ infinite?
- evinda
- · Replies 6 ·
Convergence and existence of constants
- evinda
- · Replies 6 ·
Are my ideas as for the convergence right?
- evinda
- · Replies 6 ·
Does the sequence $(a^n b^{n^2})$ converge for all values of $a$ and $b$?
- evinda
- · Replies 6 ·
Doesn't it suffice to pick the limit of the sequence?
- evinda
- · Replies 4 ·
Undergrad Showing that a_n > 0 given its decreasing and lim a_n=0
- Mr Davis 97
- · Replies 1 ·
Undergrad Searcoid corollary 1.4.5 on ordinals and proper subsets
- Math Amateur
- · Replies 4 ·
Undergrad Can ordinals α and β be disjoint in Searcoid Theorem 1.4.6?
- Math Amateur
- · Replies 2 ·
Undergrad Showing that an infinite sum converges when a sign in the denominator is flipped
- Mr Davis 97
- · Replies 11 ·
Undergrad Limsup(a+b) = limsup(a) + limsup(b)
- Mr Davis 97
- · Replies 3 ·
Undergrad Principal branch of the log function
- Measle
- · Replies 1 ·
Undergrad Searcoid Theorem 1.4.4: minimality of β in α \ x
- Math Amateur
- · Replies 2 ·
Undergrad Equality in the trichotomy for totally ordered ordinals
- Math Amateur
- · Replies 2 ·
Finding Supremum and Infimum of Sets with Inequalities
- evinda
- · Replies 15 ·
Undergrad How Do We Prove a Subset of an Ordinal is Well-Ordered?
- Math Amateur
- · Replies 2 ·
Undergrad Series of even and odd subsequences converge
- Mr Davis 97
- · Replies 16 ·
What is the Property of Infimum for Sets?
- evinda
- · Replies 8 ·
Are least upper bound and greatest lower bound properties equivalent?
- evinda
- · Replies 4 ·
Problems for Cauchy Integral Formula
- shirokuma
- · Replies 1 ·
Undergrad Learning the theory of the n-dimensional Riemann integral
- AltairAC
- · Replies 5 ·
Is Φ a Bijective Map from Power Set to Characteristic Functions?
- mathmari
- · Replies 7 ·
Undergrad How Is Divergence to Infinity Defined in Contrast to General Divergence?
- Mr Davis 97
- · Replies 3 ·
Undergrad What does the edge of a Möbius strip look like when projected onto a 2D plane?
- YoungPhysicist
- · Replies 3 ·
Undergrad Complex exponential to a power
- Mr Davis 97
- · Replies 4 ·
Proving that solutions of a equation are irrational
- ranga519
- · Replies 2 ·