16:47Any reparametrization of a regular curve is regularUnit speed curve is regularPure maths with Usama1.4K views·2 years ago
20:15ReparametrizationAny regular curve admits a reparametrization in terms of arc lengthPure maths with Usama483 views·2 years ago
28:19Arc length function for a parametrized curve speed of a curveUnit speed curvePure maths with Usama232 views·2 years ago
18:07Tangent vector of a parametrized curveFunction of class n and class infinitySmooth functionPure maths with Usama114 views·2 years ago
15:18Differential geometryParametrization Parameterized curve Level curveAstroidIMM-LUMSPure maths with Usama510 views·2 years ago
14:03Automorphisms of cyclic group of order nZnCnAut(Cp) Automorphisms of Z4, Z5 and Z6Pure maths with Usama1.7K views·3 years ago
17:24The dual space of l^p space is l^q space where p and q are conjugate indexSequence spacePure maths with Usama1.9K views·3 years ago
31:24Isometric isomorphismDual space of R^n is R^nDual space of l1 is l infinity Algebraic dual spacePure maths with Usama2.4K views·3 years ago
12:51Space of all bounded linear operatorsDual spaceB(X,Y) is a Banach space if Y is Banach spacePure maths with Usama840 views·3 years ago
15:39Dimension of Algebraic dual space A finite dimensional vector space is algebraically reflexivePure maths with Usama795 views·3 years ago
13:47Dual basis for Algebraic dual space Linear functional Kronecker Delta ExamplesPure maths with Usama386 views·3 years ago
27:05Every linear operator on a finite dimensional vector spaces represent a matrix and vise versaMatrixPure maths with Usama264 views·3 years ago
19:57Let S be a closed subspace of a Banach space N.Then NS is also a Banach spaceFunctional AnalysisPure maths with Usama672 views·3 years ago
14:34Quotient spaceHyperplaneIf S is closed subspace of a normed space then NS is also a normed spacePure maths with Usama782 views·3 years ago
18:52Convex HullConvex Hull is collection of all Linear Convex combinations Closure of a convex setPure maths with Usama498 views·3 years ago
14:43For any normed space, the open and closed balls are convex Convex SetPure maths with Usama1.7K views·3 years ago
23:39Convex Setimage of a convex Set under linear transformation is convexEvery subspace is convexPure maths with Usama763 views·3 years ago
20:03formula to find total no of permutations conjugate with α . Conjugacy classes of Symmetric group SnPure maths with Usama560 views·3 years ago
8:57Let Sn be a symmetric group. Total no of cycles of length m in Sn is n!m(n-m)! i.e. npmmPure maths with Usama229 views·3 years ago
16:33Baire's category theoremEvery Countable intersection of dense open sets is densePure maths with Usama898 views·3 years ago
17:49Order structure of S4 and S5Formula to find total no of elements of order r in S4 and S5Pure maths with Usama200 views·3 years ago
22:52Baire's Category theoremA complete metric space is of second categoryIsolated pointPure maths with Usama862 views·3 years ago
12:17First category and second categoryQ is of first categoryZ is of second category as a subspacePure maths with Usama541 views·3 years ago
19:32Nowhere dense subsetClosure of A has empty interiorcomplement of closure of A is dense in XPure maths with Usama750 views·3 years ago
16:00C[a,b] space of all continuous functions is complete C[0,1] is incomplete metric spacePure maths with Usama5.6K views·3 years ago
24:12The space R^n(or C^n) is completeThe space ℓ∞ of all bounded sequences is completePure maths with Usama495 views·3 years ago
11:53The space R with the usual metric is a complete spacePure maths with Usama1.5K views·3 years ago
10:07The space C of complex numbers with the usual metric is a complete metric spacePure maths with Usama886 views·3 years ago