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 can we compare the lower envelope of a function with the function itself?
- joypav
- · Replies 1 ·
Lower semicontinuity and step functions on intervals
- joypav
- · Replies 4 ·
How Can We Approximate a Continuous Function with a Piece-Wise Linear Function?
- joypav
- · Replies 7 ·
Graduate How to prove that cuboids are Lebesgue measurable?
- Maxi1995
- · Replies 6 ·
Every Closed Set in R has a Countable Dense Subset
- joypav
- · Replies 7 ·
Plus or minus question for the complex log
- cbarker1
- · Replies 1 ·
Undergrad Ambiguities in interpreting the ellipsis notation
- Stephen Tashi
- · Replies 12 ·
Can I Find Examples for Continuous Improvement?
- Joe20
- · Replies 1 ·
Finding limit of cos(x) using inequalities
- Joe20
- · Replies 1 ·
Undergrad Complex analysis - removable singular points
- dyn
- · Replies 5 ·
Undergrad Distribute Limit over Addition: Evaluating w/o Knowing Convergence
- Mr Davis 97
- · Replies 8 ·
Graduate Graph or lattice topology discretization
- diegzumillo
- · Replies 3 ·
Examples of the Cauchy-Schwarz inequality
- Joe20
- · Replies 1 ·
Is Showing One ε Enough to Prove Discontinuity?
- Joe20
- · Replies 3 ·
Proving continuity of sin x / x at x equals 0
- Joe20
- · Replies 2 ·
Undergrad Prove this inequality involving metrics
- TMO
- · Replies 1 ·
Undergrad Can Cauchy's Integral Formula be Used for Non-Analytic Functions?
- dyn
- · Replies 6 ·
Graduate What uniquely characterizes the germ of a smooth function?
- lugita15
- · Replies 5 ·
Undergrad Equivalence of Covering Maps and Quotient Maps
- nigelscott
- · Replies 9 ·
Undergrad Intuition - Cauchy integral theorem
- tiago23
- · Replies 4 ·
Real Analysis, Sequences in relation to Geometric Series and their sums
- joypav
- · Replies 3 ·
Set of points on the complex plane
- cbarker1
- · Replies 1 ·
Proving Modulus Inequality for Complex Numbers
- cbarker1
- · Replies 3 ·
Real Analysis, liminf/limsup inequality
- joypav
- · Replies 2 ·
Does the Norm of a Linear Integral Operator Equal Its Spectral Radius?
- sarrah1
- · Replies 1 ·
Undergrad How Does the Bernstein-Schröder Theorem Establish Set Equivalence?
- Wendel
- · Replies 1 ·
Graduate Higher Order Derivative Test and Germs
- lugita15
- · Replies 5 ·
Undergrad Why repeat the uniqueness argument in extending continuous functions
- Terrell
- · Replies 10 ·
Prove Inequality: $f(x)$ Continuous Positive $\int_{0}^{1}$
- lfdahl
- · Replies 6 ·
Undergrad Does Im[A+B+Te^{2ip}]=0 follow from the given constraints?
- AtoZ
- · Replies 14 ·
Undergrad Why does the branch cut argument give a factor of 2πi in contour integrals?
- TMO
- · Replies 5 ·
Undergrad Topology vs Differential Geometry
- Bill2500
- · Replies 7 ·
Undergrad Munkres theorem 20.1: volume under linear transformations
- Bill2500
- · Replies 5 ·
Undergrad Coordinate functions of a many-to-1 function
- Stephen Tashi
- · Replies 7 ·
Insights Hilbert Spaces and Their Relatives - Definitions
- fresh_42
- · Replies 2 ·
Undergrad Uniqueness of tangent space at a point
- kent davidge
- · Replies 16 ·
Proving Injectivity of a Vector-Valued Function Using the Mean Value Theorem
- mathmari
- · Replies 12 ·
F has an uniquely defined global minimum
- mathmari
- · Replies 12 ·
Image of each open subset is open
- mathmari
- · Replies 4 ·
Graduate Is There a Boundary Point Where the Holomorphic Function Equals Zero?
- JYM
- · Replies 2 ·
High School Geometrical Test for Immersion of Klein Bottle in Higher Dimensional Manifold
- kent davidge
- · Replies 6 ·
High School Infinite dimensional Hilbert Space
- kent davidge
- · Replies 8 ·
Graduate Why Must the Constant in Hilbert Space Function B[f(x)] Be Defined as Shown?
- member 428835
- · Replies 14 ·
Undergrad What is the usefulness of topology in understanding functions?
- kent davidge
- · Replies 10 ·
Is the system uniquely solvable?
- mathmari
- · Replies 3 ·
Challenge problem #5 [Olinguito]
- Olinguito
- · Replies 2 ·
Graduate Reshetikhin-Turaev Invariant of Manifolds
- nateHI
- · Replies 1 ·
Undergrad How do you find the Lipschitz constant for a function?
- mertcan
- · Replies 17 ·
Undergrad Why define neighborhoods by inclusion rather than containment
- mr.tea
- · Replies 12 ·
Undergrad Is dfx(y) a dual vector due to linear transformation properties?
- LagrangeEuler
- · Replies 1 ·
Calculating the Inverse Laplace Transform for a Given Function
- evinda
- · Replies 10 ·
Undergrad Why does the closure of a ball stay in a dense open set in Baire's theorem?
- mr.tea
- · Replies 3 ·
Approximation theorem of Weierstrass
- evinda
- · Replies 17 ·
Undergrad There is no relation between e and π
- the_pulp
- · Replies 7 ·
Does limit of "approximate zero set" converge to the zero set?
- Vulture1991
- · Replies 1 ·
Is the Integral Finite for $n$ Fixed?
- evinda
- · Replies 4 ·
Finding the third zero of a degree 3 complex polynomial
- TheFallen018
- · Replies 3 ·
Local extrema of homogeneous degree 2 functions at roots
- mathmari
- · Replies 18 ·
Show inequality using the mean value theorem
- mathmari
- · Replies 26 ·
Undergrad What basic knowledge do I need to study topology?
- Another
- · Replies 19 ·
Graduate Are essentially bounded functions uniform limits of simple functions?
- Shaji D R
- · Replies 3 ·
Undergrad Does the Integral of Riemman Zeta Function have a meaning?
- JorgeM
- · Replies 3 ·
Linearity and continuity of maps
- mathmari
- · Replies 13 ·
Undergrad Is ##J(f)## Non-Zero in ##U## for a Bijective ##C^m## Function?
- facenian
- · Replies 1 ·
Undergrad Distributions (generalised functions) basics
- Cathr
- · Replies 9 ·
Undergrad Elementary question on composition of functions
- facenian
- · Replies 2 ·
Undergrad What Is the New Dimension in Complex Number Graphs?
- pairofstrings
- · Replies 19 ·
Undergrad Chaos like phenomena on a simple metric space?
- Zafa Pi
- · Replies 2 ·
Graduate Quotient maps, group action, open maps
- PsychonautQQ
- · Replies 32 ·
Undergrad Problem with countably compact space
- facenian
- · Replies 11 ·
Undergrad Concept behind equivalent metrics
- Ric-Veda
- · Replies 17 ·
Graduate Volume of 3-Torus: Formula and Calculations
- novice_hack
- · Replies 2 ·
Is Path-Connectivity Equivalent to Connectivity in $\mathbb{R}^2$?
- mathmari
- · Replies 3 ·
An open cover is a collection of open sets whose union contains a given subset
- mathmari
- · Replies 16 ·
On the spectral radius of bounded linear operators
- sarrah1
- · Replies 3 ·
Undergrad Proof of Alternating Series Test
- Mr Davis 97
- · Replies 3 ·
Undergrad Weak Convergence of a Certain Sequence of Functions
- fresh_42
- · Replies 2 ·
Determining the Maximum and Minimum of a Discontinuous Function $f(x,y)$
- mathmari
- · Replies 2 ·
Graduate Mathematical Structure and Mathematical Space Hierarchies
- pairofstrings
- · Replies 4 ·
Proving that $X$ is a Banach Space and $Y$ is Not
- mathmari
- · Replies 6 ·
How to Verify the Complex Integral Equals π/(1+n)?
- Tony1
- · Replies 1 ·
Undergrad Compact subspace in metric space
- facenian
- · Replies 16 ·
High School What does the 2p term mean in Euler's formula for surfaces with p holes?
- Serious Max
- · Replies 10 ·
Help with five sequences and series problems for maths
- ertagon2
- · Replies 2 ·
Undergrad R is disconnected with the subspace topology
- kent davidge
- · Replies 6 ·
High School Mistake in my complex exponentiation: where?
- nomadreid
- · Replies 2 ·
Undergrad Does ##\mathbb{S}^1## embed in ##\mathbb{R}##?
- kent davidge
- · Replies 12 ·
Undergrad Proof that a sequence has two subsequential limits
- Mr Davis 97
- · Replies 8 ·
Sequences and their limits, convergence, supremum etc.
- ertagon2
- · Replies 1 ·
Undergrad Proof that a quantity is greater than 1/2
- Mr Davis 97
- · Replies 3 ·
Gamma function is convergent and continuous
- mathmari
- · Replies 7 ·
Undergrad Proving $\lim a_n<L \implies$ There Exists $N\in \mathbb{N}$ s.t. $a_N< L$
- Mr Davis 97
- · Replies 5 ·
Undergrad Topology: Can We Use Same Function for 2 Open Sets?
- kent davidge
- · Replies 6 ·
Continuously differentiable series
- mathmari
- · Replies 9 ·
Convergence of Alternating Series and Estimation of Absolute Error
- mathmari
- · Replies 8 ·
Find Limit of $\sqrt{x}$ as $x\to c$, $c\ge 0$
- cbarker1
- · Replies 1 ·
Undergrad Proof that p is interior if p is not limit of complement
- jamalkoiyess
- · Replies 5 ·
Undergrad Supremum of averaged tail sum with linear scaling factor
- Mr Davis 97
- · Replies 3 ·
Undergrad Problem about a connected subspace
- facenian
- · Replies 5 ·
Directional and partial derivative notation in Duistermaat and Kolk
- Math Amateur
- · Replies 1 ·