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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.
MHB Limits of functions .... D&K Lemma 1.3.3 .... another question ....
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MHB Neccesity and sufficiency .... D&K Lemma 1.3.3 ....
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Graduate Covariant derivative and 'see-saw rule'
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MHB Prove that if g(f(x)) is injective then f is injective
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Undergrad What is the Difference Between an Angular Sector and a Circular Sector?
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MHB The Closure of a Set is Closed .... Lemma 1.2.10
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MHB Open Subsets of R^n .... D&K Lemma 1.2.5
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Undergrad Minimum number of moves from a to b
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MHB Can Derivatives Exist at Discontinuities of a Piecewise Function?
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Graduate Sequence induced by short exact sequence
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High School Spherical Geometry (Two dimension ) Defining a metric
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Undergrad If A is an algebra, then its uniform closure is an algebra.
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Undergrad Describing 3d Manifold Objects as a Hypersurface
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Undergrad What would it even mean to consider a "half" derivative?
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MHB Tanh is uniformly continous on R
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MHB Proving Limits of Exponential Series at Infinity
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High School Nesting of 2-Spheres & 2-Tori in Topological Spaces
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MHB Cauchy-Schwarz Inequality - Duistermaat and Kolk, CH. 1, page 4 .... ....
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MHB Multidimensional Real Analysis - Duistermaat and Kolk, Lemma 1.1.7 ....
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Undergrad Ordered lattice of topologies on the 3 point set
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High School Complex products: perpendicular vectors and rotation effects
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MHB Find a function so that the composition is continuous
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Undergrad Can We Mathematically Define Everyday Objects Like Smartphones?
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MHB Show that the function is bounded and strictly increasing
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MHB Is the Function \( f(x) = \sqrt{4 + x^2} \) Continuous Everywhere?
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MHB Complete Metric Spaces .... Conway, Analysis, Section 5.2 ....
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MHB Evaluate Case of Fresnel Integral
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Graduate What Is the Role of the Boundary Operator in p-Chains?
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High School How a Klein bottle has a 0 volume?
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Undergrad Rational sequence converging to irrational
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MHB Can we somehow modify the Lagrange form to get a tighter bound? (Curious)
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MHB Finding the Product of Distinct Roots: A Complex Challenge
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MHB Additional solution for polar form of complex number
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MHB Complex Variables - Max Modulus Inequality
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MHB Complex Variables - Solution of a System
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MHB Adjoint operator and orthogonal projection
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Undergrad Map from space spanned by 2 complex conjugate vars to R^2
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Undergrad Is simulation considered a type of quantitative analysis?
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MHB Complex Variables - Zeros of Analytic Functions
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MHB Complex Variables - Legendre Polynomial
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Graduate Torus 2-sheet covering of Klein bottle
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High School Is the trefoil knot truly unknottable or is there a way to simplify it?
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MHB Reconciling Differences in Vector-Valued Function Derivatives
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Graduate Transfinite Taylor series of exp(x) and of h(x)
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MHB Where Can I Find a Solution to Zeidler's Eigenvalue Problem?
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Graduate Why Does the Orbit Space of a Covering Map Not Necessarily Equal the Base Space?
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Undergrad Cardinality of fibers same for covering maps
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Undergrad Choosing points from a set that produce the largest polygon
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High School Square root of a negative number in a complex field
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Graduate Fundamental group of a sphere with 6 points removed
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MHB The Directional Derivative .... in Scalar Fields and Vector Fields ....
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MHB How Does Definition 8.9 Imply Differentiability Near Point p?
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MHB Differentiation of Vector Valued Functions - Browder, Proposition 8.12 ....
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Graduate 8.12 in Browder's "Mathematical Analysis: An Introduction"
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MHB Does the Sequence Converge?
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MHB Why Does Lemma 8.4 Equal This Expression?
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MHB Why Does Theorem 1.9 Use f(t) Instead of f(γ(t))?
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Graduate Connected sum of manifolds and free group isomorphisms
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MHB Recifiable Paths in C .... Conway, Section 1, Ch. 4 ....
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Undergrad Why can we define sequences in this fashion?
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Insights The Different Faces Of The Special Unitary Group ##SU(2)##
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MHB A complex numbers' modulus identity.
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MHB Understanding Cantor's Theorem and Diameter
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MHB Complex Valued Functions BV: John B. Conway Prop 1.3 Explained
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MHB Contour Integrals - Example 2.5, Palka, Section 2.2, Ch.4 .... ....
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Graduate Questions about Covering maps, manifolds, compactness
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MHB Understand Proposition 1.3 in Conway's Functions of Complex Variables I
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MHB Proof of Lemma 2.1, Part (vi) in Palka's Ch.4: Explaining Inequality
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MHB Properties of Contour Integrals - Palka Lemma 2.1 (vi) .... ....
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MHB How Can \dot{\gamma}(0) Fail to Exist in Palka's Example 1.3?
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Undergrad Where can I find a proof of the Swiss cheese theorem?
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MHB How does Conway's Theorem 2.29 Derive the Simplified Expression for f(z)?
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Insights Representations Of The Special Unitary Group SU(2)
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MHB Complex number geometrical problem
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MHB Mapping of a Circle in the Complex Plane
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MHB Proof of Divergence: (-1)^n Sequence
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MHB Do we distinguish cases for n?
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MHB Analytic Functions - Palka, Ch. III, Section 1.3 ....
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High School Understanding the Inconsistencies of Imaginary Numbers
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MHB How Can We Prove the Modified Bernoulli Inequality?
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Graduate Fundamental group of n connect tori with one point removed
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Undergrad Intuition behind induced homomorphism from covering maps
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Graduate Fundamental group of Project Plane with 2 points missing
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MHB Disconnected Sets .... Palka, Lemma 3.1 ....
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MHB Limits of Complex Functions .... Final Remark from Palka in Section 2.2 ....
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MHB Limits of Complex Functions .... Example from Palka ....
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MHB Continuity of Complex Functions .... ....
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Undergrad Impossible to lift the identity map on the circle
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Undergrad Understanding Compactness in ##R^2##: Analyzing Boundaries and Open Disks
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Undergrad Retract of a connected space is connected
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Undergrad Proof that retract of Hausdorff space is closed
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Undergrad How Does Closure in a Neighborhood Imply Membership in a Set?
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MHB The Residue Theorem To Evaluate Integrals
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Undergrad Is S^2 - {N} Homeomorphic to R^2?
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MHB Using Residue Theorem To Prove Value Of Summation
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Undergrad Euler Characteristic of the Projective plane and sphere?
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Undergrad What is an atlas for a torus manifold?
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MHB Theorem 1.8: Sets or Domains in the Complex Plane - Palka Ch.2
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MHB Why Does γ(t) = z(1-t) Represent the Same Curve in Reverse?
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Undergrad Homotopy Class vs Fundamental Group.
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