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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Is the Absolute Convergence Theorem Sufficient to Prove This?
- alexmahone
- · Replies 1 ·
Graduate Weakly sequentially compact supsets
- rlukach
- · Replies 2 ·
Graduate Is an Open Interval Homeomorphic to R?
- fleazo
- · Replies 7 ·
Undergrad Complex conjugate of absolute exponential
- vg8open
- · Replies 7 ·
Struggling with Fourier Transform Eigenvalues?
- Stephen88
- · Replies 3 ·
Complex integral oriented counterclockwise
- Dustinsfl
- · Replies 5 ·
Evaluating Complex Integration I_c |z^2|
- AkilMAI
- · Replies 6 ·
Power Series Expansion: Solving for 1/1+z at z=-5 with Radius of Convergence
- Stephen88
- · Replies 11 ·
Show that C.R conditions are held.
- Also sprach Zarathustra
- · Replies 4 ·
Proof of Cauchy Sequence for $\{a_n\}$ Defined by $f(x)$
- alexmahone
- · Replies 6 ·
Proofs of Supremum Problem in $\mathbb{R}$
- alexmahone
- · Replies 10 ·
Another supremum and infimum problem
- alexmahone
- · Replies 5 ·
How Does Scaling a Set Affect Its Supremum and Infimum?
- alexmahone
- · Replies 2 ·
Proof of $A\subseteq B\implies\sup A\le\sup B$
- alexmahone
- · Replies 2 ·
How Does Complex Analysis Explain Geometry and Entire Functions?
- Markov2
- · Replies 8 ·
Graduate One-point compactification of space of matrices with positive trace
- julian
- · Replies 6 ·
When does a complex function have a simple zero on a given interval?
- Markov2
- · Replies 10 ·
How Does Complex Function Behavior Constrain Within and Outside the Unit Disk?
- Markov2
- · Replies 14 ·
Understanding Complex Functions and Polynomials in the Complex Plane
- Markov2
- · Replies 6 ·
Solving $\sin(z) = 2 + 3i$ using complex numbers
- Dustinsfl
- · Replies 17 ·
Analytic on D: Power Series and Polynomial Coefficients
- Dustinsfl
- · Replies 6 ·
Find principal value in a+ib form.
- paulbk108
- · Replies 6 ·
Prove $\inf \{\overline{m}-x: x\in S\}=0$
- alexmahone
- · Replies 3 ·
Can Analytic Functions Exhibit These Complex Behaviors?
- Markov2
- · Replies 9 ·
Graduate What does the frequency representation of a function show?
- Tosh5457
- · Replies 5 ·
How Do Complex Numbers Relate to the Unit Disk and Their Properties?
- Markov2
- · Replies 5 ·
Graduate Is the Pre-Image Always Open in Topological Spaces?
- Jooolz
- · Replies 6 ·
Bounded Function on Set S: Proving $|f(z)|\le1$ for All $z\in S$
- Markov2
- · Replies 10 ·
Can Analytic Functions in the Unit Disk Meet Specific Modulus Conditions?
- Markov2
- · Replies 6 ·
How Can I Create a Mobius Transformation?
- Stephen88
- · Replies 3 ·
Proving Local Maximum for Analytic Functions on Open and Connected Sets
- Markov2
- · Replies 6 ·
Proving Nested Intervals Converge to $\alpha$
- alexmahone
- · Replies 2 ·
Graduate Co-finite topology on an infinite set
- Deveno
- · Replies 2 ·
Uniform Convergence of $Y(x)$ in $(0,1]$
- Also sprach Zarathustra
- · Replies 5 ·
Expanding f(z) with Powers of z-1
- Dustinsfl
- · Replies 13 ·
Graduate Equivalent definition of the supremum
- submartingale
- · Replies 5 ·
How to prove $a_n\to 0$ using the sequence location theorem?
- alexmahone
- · Replies 4 ·
Can Complex Equations Be Solved More Efficiently?
- Markov2
- · Replies 9 ·
How do I expand $f(z)$ into a power series?
- Dustinsfl
- · Replies 12 ·
Complex Integral: Solving a Difficult Problem
- Advent
- · Replies 8 ·
Does Convergence of a Sequence Imply Convergence of Its Absolute Values?
- alexmahone
- · Replies 5 ·
What Values of z Make This Series Converge?
- Dustinsfl
- · Replies 9 ·
Holomorphic function and an open disc
- Stephen88
- · Replies 3 ·
Graduate Notation for set of limit points?
- nonequilibrium
- · Replies 2 ·
Does an Increasing Sequence Bounded by a Convergent Sequence Converge?
- alexmahone
- · Replies 2 ·
Graduate What does it mean for a space to be naturally identified with another?
- daveyp225
- · Replies 7 ·
Graduate Is a convex subset of a connected space connected?
- nonequilibrium
- · Replies 2 ·
Prove that there is a strictly decreasing sequence
- alexmahone
- · Replies 2 ·
Solving Fourrier Transform Problems: Schwartz Space & exp(-ax^2)
- AkilMAI
- · Replies 6 ·
T - Improving Upper Bound for $a_n$ in Series for $n$
- alexmahone
- · Replies 6 ·
Graduate What Does the Product of Spheres Look Like?
- Jooolz
- · Replies 13 ·
Prove that the sequence converges to 0 (2)
- alexmahone
- · Replies 2 ·
Prove that the sequence converges to 0
- alexmahone
- · Replies 3 ·
Graduate A metric space of equivalent sequence classes
- goedelite
- · Replies 11 ·
High School Complex Conjugate: just replace i by -i even in denominator or inside argument?
- aimforclarity
- · Replies 12 ·
Graduate Completeness of ℝ (when ℝ is defined abstractly)
- Fredrik
- · Replies 2 ·
Graduate Metric function composed with concave function
- shoescreen
- · Replies 5 ·
Graduate Is the Empty Set Axiom Redundant in Ultrafilters?
- alexfloo
- · Replies 6 ·
Graduate How the value of ln(-1) is derived
- Benn
- · Replies 1 ·
Graduate Looking for a metric to express difference between two curves
- meldraft
- · Replies 6 ·
Undergrad Anyone here ever got bugged with i?
- fbs7
- · Replies 61 ·
Graduate Example in topology: quotient maps and arcwise connected
- nonequilibrium
- · Replies 3 ·
Graduate Graphing a function in a Normed linear space
- bugatti79
- · Replies 2 ·
Graduate Counterexample intersections of 2 compacts is compact ?
- nonequilibrium
- · Replies 7 ·
Graduate Weak convergence of orthonormal sequences in Hilbert space
- kisengue
- · Replies 3 ·
Graduate Why category in Baire's Category Theorem?
- goedelite
- · Replies 4 ·
Undergrad Splitting an exponential complex number into real and imaginary parts
- dan5
- · Replies 2 ·
Graduate Sketching exponential curves with complex numbers
- dan5
- · Replies 4 ·
Graduate What are the biggest questions in topology and abstract algebra?
- kramer733
- · Replies 4 ·
Graduate Every uncountable subset of R has a limit point in Q?
- nonequilibrium
- · Replies 4 ·
Graduate [topology] new kind of separation axiom? where does it fit in?
- nonequilibrium
- · Replies 2 ·
Graduate Help me, nearest neighbor problem.
- phaothu365
- · Replies 2 ·
Undergrad Taking a number to a complex number power
- ucbugrad
- · Replies 3 ·
Undergrad What Does It Mean for a Function to Be Single Valued?
- Hermes10
- · Replies 4 ·
Graduate A question about subspace topolgy
- ShahidNawaz
- · Replies 6 ·
Graduate Interior Product: Find from Exterior Product
- joebohr
- · Replies 10 ·
Graduate A Question about Topological Connectivity
- RVM45
- · Replies 2 ·
Graduate Are Convergence Sequences Unique in a Normed Linear Space?
- bugatti79
- · Replies 18 ·
Graduate Verify: Topology of Point-Set Question Needs to be First Countable
- Poopsilon
- · Replies 2 ·
Graduate A problem about equivalent metric
- prophetlmn
- · Replies 3 ·
Graduate Boundary points of subsets when viewed with the subset topology
- Damidami
- · Replies 4 ·
Graduate Connecting homomorphism question
- panzervlad
- · Replies 2 ·
Graduate Help with continuous functions in metric spaces
- h20o85
- · Replies 4 ·
Undergrad Why does the graph of y = ln(x) have an imaginary part?
- rollcast
- · Replies 4 ·
Graduate Is there an interesting way to define a continuous composition of functions?
- Stephen Tashi
- · Replies 4 ·
Graduate Distance between sets (a triangle-type inequality)
- Identity
- · Replies 2 ·
Graduate Compactness is topology-independent ?
- dextercioby
- · Replies 7 ·
Graduate Group of translations on real line with discrete topology
- xboy
- · Replies 3 ·
Graduate S^2 union a line connecting the north and south pole
- mathsq
- · Replies 6 ·
Graduate How Can I Better Understand Metric Space Problems?
- Someguy25
- · Replies 2 ·
Undergrad What Determines the Angle of a Complex Number in Polar Form?
- carlodelmundo
- · Replies 2 ·
Graduate Is {X, max(d,r)} or (X, min(d,r)) a Metric Space?
- ag2ie
- · Replies 8 ·
Graduate Applied Functional Analysis by Zeidler
- _DJ_british_?
- · Replies 2 ·
Undergrad Is the complex plane meaningful?
- 1MileCrash
- · Replies 4 ·
Graduate What Should an Engineer Know Before Studying Topology?
- boneh3ad
- · Replies 20 ·
Undergrad Help proving complex inequality
- JerryG
- · Replies 1 ·
Graduate How to prove that SU(3) is compact
- zahero_2007
- · Replies 25 ·
Graduate Compactness of (0,1) when that is the whole metric space
- deckoff9
- · Replies 7 ·
Graduate Defining an Empty Set Metric Space: Understanding Properties of d
- zooxanthellae
- · Replies 7 ·
Graduate Does Convergence of (sn) and (sntn) Imply (tn) Converges?
- gsmith89
- · Replies 2 ·