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Differential Geometry

Do non-orthogonal coordinate systems mean dependent coordinates?
4.6K threads
Undergrad Do non-orthogonal coordinate systems mean dependent coordinates?
  • Sticky
Insights The Orin Fractional Calculus
  • benorin
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9
Graduate Zeros of functions analytic in 2 variables
  • Paul Colby
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6
Undergrad What is "x" in this definition of a basis?
  • Hill
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4
Graduate Knots In 4D
  • Hornbein
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2
Graduate A nice YouTube channel about all things Riemann Zeta
  • Swamp Thing
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1
Undergrad About the definition of topological manifold using closed sets
  • cianfa72
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14
Graduate Trivial fiber bundle vs product space
  • cianfa72
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31
Graduate Another similar notion to compactness
  • mad mathematician
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2
Graduate Hopf fibration of 3-sphere
  • cianfa72
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39
Graduate Shauder basis for Hilbert spaces
  • cianfa72
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0
Undergrad Finding the inverse tangent of a complex number
  • bsaucer
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3
Undergrad Apparent counterexample to Cauchy-Goursat theorem (Complex Analysis)
  • SomeBody
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7
Undergrad 2-sphere intrinsic definition by gluing disks' boundaries
  • cianfa72
  • · Replies 11 ·
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11
Undergrad Confused by proof in Hocking and Young
  • yossell
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4
Undergrad "Magic" regulating functions for divergent series
  • Swamp Thing
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3
High School How does the Riemann Hypothesis/Riemann Zeta function even work?
  • Beyond3D
  • · Replies 17 ·
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17
Graduate Question about intersection of coordinate rings
  • MathLearner123
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1
Undergrad How are the following three definitions subtly different?
  • elias001
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15
Undergrad Evaluate two complex integrals along a parabolic contour
  • elias001
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2
Undergrad Convergence not defined by any metric
  • elias001
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17
Undergrad Homemorphism in quotient topology
  • elias001
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5
Undergrad No structure in ##(d,x)## in ##\textbf{Met*}(X)## is admissible
  • elias001
  • · Replies 0 ·
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0
Undergrad A beginner’s thoughts on rotation number -- Resource suggestion request
  • Pencilvester
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6
Insights The Many Faces of Topology
  • fresh_42
  • · Replies 3 ·
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3
Undergrad (0,1) is uncountable using binary expansions?
  • psie
  • · Replies 15 ·
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15
Graduate Expansion with respect to ##z_1##
  • MathLearner123
  • · Replies 1 ·
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1
Undergrad What is the 4D Equivalent of a Möbius Strip or Klein Bottle?
  • blackholesarecool
  • · Replies 30 ·
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Undergrad In Which N-Dimensional Spaces Are Rotations Chiral?
  • Hornbein
  • · Replies 11 ·
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11
High School Functions f: ℝ --> ℝ
  • mairzydoats
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8
Undergrad How to see that cos(z) is unbounded, but cos(xy)+isin(xy) is bounded?
  • am4th
  • · Replies 8 ·
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8
Undergrad Continuity of linear map from subspace of Euclidean space
  • psie
  • · Replies 2 ·
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2
Undergrad Uniform convergence of difference quotient in higher dimensions
  • psie
  • · Replies 1 ·
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1
Graduate A complicated integral to be evaluated by complex contour method
  • Bengy
  • · Replies 14 ·
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14
Undergrad Dyadic cubes generate Borel sigma algebra of subset
  • psie
  • · Replies 2 ·
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2
High School Topological neigborhoods that are not intervals in the real line?
  • mcastillo356
  • · Replies 15 ·
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15
Undergrad Homeomorphism onto a not open image in the target
  • cianfa72
  • · Replies 2 ·
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2
Undergrad On commutativity of convolution
  • psie
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3
Undergrad A concise "proof" of the Riemann-Lebesgue lemma
  • psie
  • · Replies 1 ·
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1
Undergrad A curve that does not meet rational points
  • wrobel
  • · Replies 9 ·
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9
Undergrad Relation between a circle and line in complex plane
  • Darshit Sharma
  • · Replies 16 ·
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16
Undergrad About convergence of complex power series on the circle ##|z - z_0|=r##
  • cianfa72
  • · Replies 22 ·
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22
Graduate Information theory via knot theory
  • Twodogs
  • · Replies 15 ·
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15
Undergrad Connection between absolute continuity of function and measure
  • psie
  • · Replies 2 ·
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2
Undergrad Pointwise convergence in Lp space
  • psie
  • · Replies 1 ·
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1
Undergrad Norm of integral less than or equal to integral of norm of function
  • psie
  • · Replies 3 ·
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3
High School Continuity of ln(x) function
  • eneacasucci
  • · Replies 11 ·
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11
Undergrad How to show the diagonal in the extended plane is closed?
  • psie
  • · Replies 4 ·
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4
Undergrad Verifying pointwise convergence of indicator functions
  • psie
  • · Replies 4 ·
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4
Undergrad Measure with respect to complete measure is also complete
  • psie
  • · Replies 3 ·
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3
Undergrad Help understanding a passage from a proof of change of variables formula
  • psie
  • · Replies 1 ·
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1
Undergrad Metric Tensor on ##S^1## x ##S^2##
  • Onyx
  • · Replies 6 ·
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6
Undergrad Unit sphere is compact in 1-norm
  • psie
  • · Replies 3 ·
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3
Undergrad Zero raised to a positive real number
  • psie
  • · Replies 12 ·
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12
Undergrad Exercise 2.23 in Folland's real analysis text
  • psie
  • · Replies 2 ·
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2
Undergrad Does Ricci Flow Contract a 3-Sphere to Its Center?
  • casparov
  • · Replies 1 ·
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1
Undergrad On base-b expansion of nonnegative reals
  • psie
  • · Replies 7 ·
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7
Undergrad On translation and dilation invariant Lebesgue measure: Folland's text
  • psie
  • · Replies 2 ·
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2
Undergrad Simple partitioning of sequence in Proposition 1.15 in Folland's text
  • psie
  • · Replies 3 ·
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3
Undergrad Regarding dominated convergence theorem in Folland
  • psie
  • · Replies 5 ·
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5
Undergrad On Borel sets of the extended reals
  • psie
  • · Replies 2 ·
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2
High School Can Riemann integrable be defined using the epsilon delta non method?
  • hongseok
  • · Replies 5 ·
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5
Undergrad Basic question on 'bounded implies totally bounded'
  • psie
  • · Replies 16 ·
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16
Undergrad Open balls dense in closed balls in Euclidean space
  • psie
  • · Replies 2 ·
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2
Insights Views On Complex Numbers
  • fresh_42
  • · Replies 108 ·
4
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108
Undergrad Show that a "cross" is not a topological manifold
  • cianfa72
  • · Replies 20 ·
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20
Undergrad Tough lemma on locally finite refinement
  • Korybut
  • · Replies 8 ·
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8
Insights Aspects Behind the Concept of Dimension in Various Fields
  • fresh_42
  • · Replies 2 ·
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2
Graduate Cubical cup poduct with a unit 1-cochain and the coboundary operator
  • CoreSpace
  • · Replies 0 ·
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0
Undergrad Opinion about an introduction of the Lebesgue integral in "Introduction to Hilbert spaces with applications"
  • Cauer
  • · Replies 5 ·
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5
Undergrad Compact support functions and law of a random variable
  • psie
  • · Replies 11 ·
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11
Undergrad Question about partial derivative relations for complex numbers
  • binbagsss
  • · Replies 9 ·
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9
Undergrad Uniform closure of algebra of bounded functions is uniformly closed
  • psie
  • · Replies 2 ·
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2
Undergrad Parallel rectangles contained in oblique rectangle
  • psie
  • · Replies 5 ·
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5
Graduate Question about different statements of Picard Theorem
  • MathLearner123
  • · Replies 0 ·
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0
Undergrad Question about convex property in Jensen's inequality
  • psie
  • · Replies 4 ·
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4
Undergrad A non-empty intersection of closures of level sets implies discontinuity
  • pasmith
  • · Replies 1 ·
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1
Graduate Proving that this integral is divergent
  • cbarker1
  • · Replies 2 ·
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2
Graduate Question about covering map of punctured unit disk
  • MathLearner123
  • · Replies 3 ·
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3
Graduate Question about lifting of a function
  • MathLearner123
  • · Replies 2 ·
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2
Graduate Question about existence of path-lifting property
  • MathLearner123
  • · Replies 8 ·
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8
Undergrad Riemann integrability and uniform convergence
  • lys04
  • · Replies 2 ·
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2
Integration in Polar Coordinates (Fubini/Tonelli)
  • joypav
  • · Replies 4 ·
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4
Undergrad On theorem 1.19 in Folland's and completion of measure
  • psie
  • · Replies 1 ·
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1
Undergrad Formal definition of multiplication for real and complex numbers
  • logicgate
  • · Replies 2 ·
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2
High School Identity Theorem for power series
  • Hill
  • · Replies 10 ·
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10
Undergrad Are slices of measurable functions measurable?
  • Office_Shredder
  • · Replies 3 ·
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3
Undergrad Post your favorite real analysis problem
  • docnet
  • · Replies 5 ·
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5
Undergrad On integral of simple function and representation
  • psie
  • · Replies 6 ·
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6
Undergrad Collection of finite unions of half-open intervals form an algebra
  • psie
  • · Replies 3 ·
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3
Undergrad How Does the Hopf Map Relate to Foliation and Knot Theory on the 3-Torus?
  • Anko
  • · Replies 8 ·
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8
Undergrad Help with basic transfinite induction proof
  • psie
  • · Replies 2 ·
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2
Undergrad On two definitions of locally compact
  • psie
  • · Replies 5 ·
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5
Undergrad Showing equivalence of two definitions of essential supremum
  • psie
  • · Replies 1 ·
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1
Undergrad Two basic results from measure theory -- on volumes of rectangles
  • psie
  • · Replies 2 ·
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2
Undergrad In which sense(s) do square integrable functions go to zero at infinity?
  • gentzen
  • · Replies 2 ·
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2
Graduate Functional Analysis for Physics in 2024
  • psterphysics
  • · Replies 11 ·
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11
Undergrad Question about branch of logarithms
  • MathLearner123
  • · Replies 14 ·
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14
Graduate Can Equilibrium State Determine Complex Potential?
  • binbagsss
  • · Replies 5 ·
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5
High School Finite linear combination of continuous functions is continuous?
  • docnet
  • · Replies 3 ·
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3
Undergrad Verify the completion of continuous compactly supported functions
  • psie
  • · Replies 4 ·
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4
Undergrad Fiber bundle homeomorphism with the fiber
  • cianfa72
  • · Replies 43 ·
2
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43