Topology and Analysis Forum

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.

Threads

Graduate How to prove that cuboids are Lebesgue measurable?

  • Maxi1995
  • · Replies 6 ·
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6

Every Closed Set in R has a Countable Dense Subset

  • joypav
  • · Replies 7 ·
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7

Plus or minus question for the complex log

  • cbarker1
  • · Replies 1 ·
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1

Undergrad Ambiguities of the "...." notation

  • Stephen Tashi
  • · Replies 12 ·
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12

Can I Find Examples for Continuous Improvement?

  • Joe20
  • · Replies 1 ·
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1

Find Limit of cos(x) with Inequalities | Part (b) Help

  • Joe20
  • · Replies 1 ·
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1

Undergrad Complex analysis - removable singular points

  • dyn
  • · Replies 5 ·
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5

Undergrad Distribute Limit over Addition: Evaluating w/o Knowing Convergence

  • Mr Davis 97
  • · Replies 8 ·
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8

Graduate Graph or lattice topology discretization

  • diegzumillo
  • · Replies 3 ·
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3

Understanding the Cauchy-Schwarz Inequality

  • Joe20
  • · Replies 1 ·
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1

Is Showing One ε Enough to Prove Discontinuity?

  • Joe20
  • · Replies 3 ·
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3

Can Dividing by Sin x Help Prove Continuity at x = 0?

  • Joe20
  • · Replies 2 ·
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2

Undergrad Prove this inequality involving metrics

  • TMO
  • · Replies 1 ·
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1

Undergrad Can Cauchy's Integral Formula be Used for Non-Analytic Functions?

  • dyn
  • · Replies 6 ·
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6

Graduate What uniquely characterizes the germ of a smooth function?

  • lugita15
  • · Replies 5 ·
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5

Undergrad Equivalence of Covering Maps and Quotient Maps

  • nigelscott
  • · Replies 9 ·
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9

Undergrad Intuition - Cauchy integral theorem

  • tiago23
  • · Replies 4 ·
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4
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3

Set of points on the complex plane

  • cbarker1
  • · Replies 1 ·
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1

Proving Modulus Inequality for Complex Numbers

  • cbarker1
  • · Replies 3 ·
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3

Real Analysis, liminf/limsup inequality

  • joypav
  • · Replies 2 ·
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2

Does the Norm of a Linear Integral Operator Equal Its Spectral Radius?

  • sarrah1
  • · Replies 1 ·
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1

Undergrad How Does the Bernstein-Schröder Theorem Establish Set Equivalence?

  • Wendel
  • · Replies 1 ·
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1

Graduate Higher Order Derivative Test and Germs

  • lugita15
  • · Replies 5 ·
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5

Undergrad Proof Explanation: Showing an extension to a continuous function

  • Terrell
  • · Replies 10 ·
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10

Prove Inequality: $f(x)$ Continuous Positive $\int_{0}^{1}$

  • lfdahl
  • · Replies 6 ·
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6

Undergrad Verifying Equality: \mathcal{Im}[A+B+Te^{2ip}]=0

  • AtoZ
  • · Replies 14 ·
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14

Undergrad Understanding the "branch cut argument"

  • TMO
  • · Replies 5 ·
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5

Undergrad Topology vs Differential Geometry

  • Bill2500
  • · Replies 7 ·
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7

Undergrad Munkres-Analysis on Manifolds: Theorem 20.1

  • Bill2500
  • · Replies 5 ·
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5

Undergrad Coordinate functions of a many-to-1 function

  • Stephen Tashi
  • · Replies 7 ·
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7

Insights Hilbert Spaces and Their Relatives - Definitions

  • fresh_42
  • · Replies 2 ·
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2

Undergrad Uniqueness of tangent space at a point

  • kent davidge
  • · Replies 16 ·
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16
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12

F has an uniquely defined global minimum

  • mathmari
  • · Replies 12 ·
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12

Image of each open subset is open

  • mathmari
  • · Replies 4 ·
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4

Graduate Is There a Boundary Point Where the Holomorphic Function Equals Zero?

  • JYM
  • · Replies 2 ·
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2

High School Geometrical Test for Immersion of Klein Bottle in Higher Dimensional Manifold

  • kent davidge
  • · Replies 6 ·
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6

High School Infinite dimensional Hilbert Space

  • kent davidge
  • · Replies 8 ·
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8

Graduate Why Must the Constant in Hilbert Space Function B[f(x)] Be Defined as Shown?

  • member 428835
  • · Replies 14 ·
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14

Undergrad What is the usefulness of topology in understanding functions?

  • kent davidge
  • · Replies 10 ·
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10

Is the system uniquely solvable?

  • mathmari
  • · Replies 3 ·
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3

Challenge problem #5 [Olinguito]

  • Olinguito
  • · Replies 2 ·
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2

Graduate Reshetikhin-Turaev Invariant of Manifolds

  • nateHI
  • · Replies 1 ·
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1

Undergrad Lipschitz Condition: Finding the Lipschitz Constant

  • mertcan
  • · Replies 17 ·
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17

Undergrad Defining Neighborhoods in Topology: Inclusion vs. Containment

  • mr.tea
  • · Replies 12 ·
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12

Undergrad Is dfx(y) a dual vector due to linear transformation properties?

  • LagrangeEuler
  • · Replies 1 ·
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1

Calculating the Inverse Laplace Transform for a Given Function

  • evinda
  • · Replies 10 ·
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10

Undergrad Baire Category Theorem: Question About Countable Dense Open Sets

  • mr.tea
  • · Replies 3 ·
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3

Approximation theorem of Weierstrass

  • evinda
  • · Replies 17 ·
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17

Undergrad There is no relation between e and π

  • the_pulp
  • · Replies 7 ·
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7

Does limit of "approximate zero set" converge to the zero set?

  • Vulture1991
  • · Replies 1 ·
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1

Is the Integral Finite for $n$ Fixed?

  • evinda
  • · Replies 4 ·
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4

Can you help me find the third zero of this complex polynomial?

  • TheFallen018
  • · Replies 3 ·
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3

Deriving Extremas of Homogeneous Functions: A Chain Rule Comparison

  • mathmari
  • · Replies 18 ·
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18

Show inequality using the mean value theorem

  • mathmari
  • · Replies 26 ·
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26

Undergrad What are the essential foundations for studying topology?

  • Another
  • · Replies 19 ·
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19

Graduate Essentially bounded functions and simple functions

  • Shaji D R
  • · Replies 3 ·
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3

Undergrad Does the Integral of Riemman Zeta Function have a meaning?

  • JorgeM
  • · Replies 3 ·
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3

Linearity and continuity of maps

  • mathmari
  • · Replies 13 ·
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13

Undergrad Is ##J(f)## Non-Zero in ##U## for a Bijective ##C^m## Function?

  • facenian
  • · Replies 1 ·
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1

Undergrad Distributions (generalised functions) basics

  • Cathr
  • · Replies 9 ·
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9

Undergrad Elementary question on composition of functions

  • facenian
  • · Replies 2 ·
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2

Undergrad What Is the New Dimension in Complex Number Graphs?

  • pairofstrings
  • · Replies 19 ·
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19

Undergrad Chaos like phenomena on a simple metric space?

  • Zafa Pi
  • · Replies 2 ·
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2

Graduate Quotient maps, group action, open maps

  • PsychonautQQ
  • · Replies 32 ·
2
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32

Undergrad Problem with countably compact space

  • facenian
  • · Replies 11 ·
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11

Undergrad Concept behind equivalent metrics

  • Ric-Veda
  • · Replies 17 ·
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17

Graduate Volume of 3-Torus: Formula and Calculations

  • novice_hack
  • · Replies 2 ·
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2

Is Path-Connectivity Equivalent to Connectivity in $\mathbb{R}^2$?

  • mathmari
  • · Replies 3 ·
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3
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16

On the spectral radius of bounded linear operators

  • sarrah1
  • · Replies 3 ·
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3

Undergrad Proof of Alternating Series Test

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad Weak Convergence of a Certain Sequence of Functions

  • fresh_42
  • · Replies 2 ·
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2

Determining the Maximum and Minimum of a Discontinuous Function $f(x,y)$

  • mathmari
  • · Replies 2 ·
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2

Graduate Mathematical Structure and Mathematical Space Hierarchies

  • pairofstrings
  • · Replies 4 ·
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4

Proving that $X$ is a Banach Space and $Y$ is Not

  • mathmari
  • · Replies 6 ·
Replies
6

How to Verify the Complex Integral Equals π/(1+n)?

  • Tony1
  • · Replies 1 ·
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1

Undergrad Compact subspace in metric space

  • facenian
  • · Replies 16 ·
Replies
16

High School Understanding V-E+F=2-2p: An Explanation from What is Mathematics by Courant

  • Serious Max
  • · Replies 10 ·
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10

Solve Maths Sequences & Series - Get Passing Grade Now

  • ertagon2
  • · Replies 2 ·
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2

Undergrad R is disconnected with the subspace topology

  • kent davidge
  • · Replies 6 ·
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6

High School Mistake in my complex exponentiation: where?

  • nomadreid
  • · Replies 2 ·
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2

Undergrad Does ##\mathbb{S}^1## embed in ##\mathbb{R}##?

  • kent davidge
  • · Replies 12 ·
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12

Undergrad Proof that a sequence has two subsequential limits

  • Mr Davis 97
  • · Replies 8 ·
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8

Sequences and their limits, convergence, supremum etc.

  • ertagon2
  • · Replies 1 ·
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1

Undergrad Proof that a quantity is greater than 1/2

  • Mr Davis 97
  • · Replies 3 ·
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3

Gamma function is convergent and continuous

  • mathmari
  • · Replies 7 ·
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7

Undergrad Proving $\lim a_n<L \implies$ There Exists $N\in \mathbb{N}$ s.t. $a_N< L$

  • Mr Davis 97
  • · Replies 5 ·
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5

Undergrad Topology: Can We Use Same Function for 2 Open Sets?

  • kent davidge
  • · Replies 6 ·
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6

Continuously differentiable series

  • mathmari
  • · Replies 9 ·
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9

Convergence of Alternating Series and Estimation of Absolute Error

  • mathmari
  • · Replies 8 ·
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8

Find Limit of $\sqrt{x}$ as $x\to c$, $c\ge 0$

  • cbarker1
  • · Replies 1 ·
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1

Undergrad Proof that p is interior if p is not limit of complement

  • jamalkoiyess
  • · Replies 5 ·
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5

Undergrad Clarification of a line in a proof

  • Mr Davis 97
  • · Replies 3 ·
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3

Undergrad Problem about a connected subspace

  • facenian
  • · Replies 5 ·
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5

Directional and Partial Derivatives ....Notation .... D&K ....

  • Math Amateur
  • · Replies 1 ·
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1

High School Can Irrational Numbers Ever Align in a Theoretical Game?

  • AplanisTophet
  • · Replies 14 ·
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14

Undergrad Understanding metric space definition through concrete examples

  • Ricster55
  • · Replies 3 ·
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3

Undergrad Why Are Topology Axioms Defined the Way They Are?

  • kent davidge
  • · Replies 1 ·
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1