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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 Proposition 2.2.9: Understanding the Implication of Lemma 1.1.7 (iv) for Peter
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MHB Total Derivatives and Linear Mappings .... D&K Example 2.2.5 ....
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I Total Derivatives and Linear Mappings .... D&K Example 2.2.5
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MHB Differentials in Multivariable Functions .... Kantorovitz: Example 4, page 66
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I Differentials in Multivariable Functions ....
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MHB The Differentail and the Derivative in Multivariable Analysis .... ....
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I Differential for Real Valued Functions of Several Variables
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MHB Solving Kantorovitz' Example 3 on Real Valued Functions of Several Variables
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I Directional & Partial Derivatives .... working from the definition
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I Existence of Partial Derivatives and Continuity ....
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I Turning the square into a circle
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MHB How does Lemma 2.2.3 Demonstrate the Uniqueness of the Derivative?
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MHB Differentiability of mappings from R^n to R^p .... .... D&K Defn 2.2.2 ....
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MHB Axis Through x in the direction u .... in R^k .... ....
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A Can Alexander Duality Help Compute the Homology Groups of R^3 Minus a Tube?
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MHB Differentiability of mappings from R to R .... ....
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MHB The Heine-Borel Theorem in R^n .... .... D&K Theorem 1.8.17 .... ....
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MHB Definition of Connectedness .... What's wrong with my informal thinking ....?
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I Importance of Archimedean Property and Density of Rationals
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MHB Show that a sequence is bounded, monotone, using The Convergence Theorem
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MHB Heine-Borel Theorem & D&K Theorem 1.8.17 | Peter's Question
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MHB Compactness and Uniform Continuity in R^n .... .... D&K Theorem 1.8.15
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MHB Linear Mappings are Lipschitz Continuous .... D&K Example 1.8.14 .... ....
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MHB The Euclidean Norm is Lipschitz Continuous .... D&K Example 1.3.5 .... ....
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MHB Reference request - Measure theory
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MHB Norms in R^n .... and Aut(R^n) .... .... D&K Corollary 1.8.12 .... ....
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MHB Equivalence of Norms in R^n .... D&K Corollary 1.8.10 .... ....
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MHB Lipschitz Continuity .... and Continuity in R^n ....
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MHB Compactness and Continuity in R^n .... .... D&K Theorem 1.8.8 .... ....
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MHB Open and Closed in V .... D&K Proposition 1.2.17 .... ....
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MHB Prove the Following is True About the Complex Function f(z) = e^1/z
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MHB Another question on Open and Closed in V .... D&K Proposition 1.2.17 .... ....
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MHB A Further Question on Proper and Continuous Mappings .... D&K Theorem 1.8.6 ....
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MHB Proper and Continuous Mappings in R^n .... ....
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MHB Compact Sets and Closed Sets in R^n .... .... D&K Lemma 1.8.2 .... ....
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MHB Compact Sets in R^n .... .... D&K Theorem 1.8.4 .... ....
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MHB Cauchy Sequences and Completeness in R^n ....
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MHB Subsequences and Limits in R and R^n .... .... L&S Theorem 5.2 .... ....
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MHB Coordinate-Wise Convergence in R^n .... TB&B Chapter 11, Section 11.4 ....
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I Equidistance of Points in a Sphere?
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MHB Proof of Bolzano-Weierstrass on R .... .... D&K Theorem 1.6.2 .... ....
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MHB Orthogonal Projection .... .... D&K Example 1.5.3 .... ....
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MHB How Do You Calculate the Real and Imaginary Parts of \( e^{e^z} \)?
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MHB Continuous Functions and Open Sets .... D&K Example 1.3.8 ....
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A How can I Prove the following Integral Inequality?
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A How to find the domain of functions of an operator
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MHB [Complex Analysis] Singularity in product of analytic functions
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MHB How is the remainder for Taylor polynomials calculated?
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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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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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I 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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I 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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A Sequence induced by short exact sequence
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B Spherical Geometry (Two dimension ) Defining a metric
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I If A is an algebra, then its uniform closure is an algebra.
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I Describing 3d Manifold Objects as a Hypersurface
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I 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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B 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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I Ordered lattice of topologies on the 3 point set
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MHB Find a function so that the composition is continuous
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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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A What Is the Role of the Boundary Operator in p-Chains?
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MHB Can we somehow modify the Lagrange form to get a tighter bound? (Curious)
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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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I Map from space spanned by 2 complex conjugate vars to R^2
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I 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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A Torus 2-sheet covering of Klein bottle
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B 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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A 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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A Why Does the Orbit Space of a Covering Map Not Necessarily Equal the Base Space?
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I Cardinality of fibers same for covering maps
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I Choosing points from a set that produce the largest polygon
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A 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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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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A 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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