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- Metric Spaces (Notes)
- ometric and example * Distance between sets * Theorem: Let $(X,d)$ be a metric space. Then for any $x,y... \,y).$$ * Diameter of a set * Bounded Set * Theorem: The union of two bounded set is bounded. * Ope... closed ball, sphere and examples * Open Set * Theorem: An open ball in metric space //X// is open. * Limit point of a set * Closed Set * Theorem: A subset //A// of a metric space is closed if an
- Real Analysis Notes by Prof Syed Gul Shah
- Sequence * Convergence of the Sequence * Theorem: A convergent sequence of real number has one and... sequence is unique.) * Cauchy Sequence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem: If $s_n<u_n<t_n$ for all $n\ge n_0$ and if both ... the sequence $\{u_n\}$ also converges to s. * Theorem: If the sequence $\{s_n\}$ converges to //s// the
- Advance Functional Analysis by Waseem Akram
- in functional analysis, including the Hahn-Banach Theorem, Baire Category Theorem, Open Mapping Theorem, Closed Graph Theorem, and Banach Fixed Point Theorem. The presentation is somewhat informal, with occasio
- Advance Functional Analysis by Waseem Akram
- in functional analysis, including the Hahn-Banach Theorem, Baire Category Theorem, Open Mapping Theorem, Closed Graph Theorem, and Banach Fixed Point Theorem. The presentation is somewhat informal, with occasio
- Groups (Handwritten Notes) by Atiq ur Rehman
- , isomorphism, endomorphism, examples and related theorem * Kernel, definition and related theorems * C... on and examples * Index of subgroup, Lagrange's theorem * Double coset, related theorem * Normalizer, definition and related theorems * Centralizer, centre of group, related theorem * Conjugate or transform of a group, definition
- Real Analysis Handwritten Notes by Kaushef Salamat
- * Urysohn Property * Monotone Subsequence Theorem * The Bolzano-weirstrass Theorem * Cauchy Sequence * Contractive Sequence * Properly Diverg... Sequence * Properly Divergent * Comparison Theorem </col> <col sm="6"> * Limit Inferior and... Superior * Cluster Point * Cauchy's Second theorem on Limit * Sets of Real Numbers * Heine-Bor
- Functional Analysis by Mr. Tahir Hussain Jaffery
- Finite category (or meager) * Baire's category theorem * The principal of uniform boundedness or Banach-Steinhaus theorem * Subadditive, positive homogeneous * Subli... orm * Extensions, restriction * Hahn-Banach theorem (real version) * Hahn-Banach theorem (complex version) * Hahn-Banach theorem for non-linear spaces
- Handwritten Notes of Real Analysis by Asim Marwat
- lower bound (glb), Archimedean property, density theorem, Bolzano Weierstrass theorem. * Chapter 02: Limit of the Function * Sequence, bounded sequence, Sandwhich theorem, monotone sequence, monotonic convergent theorem, nested intervals, sub-sequence, Cauchy sequence, compari
- Classical Mechanics by Muhammad Usman Hamid
- * Introduction, basic definitions. Foucault"s Theorem, Newtonian Mechanics. Fundamental laws and princi... conservative force fields, conservation of energy theorem, impulse, torque. Conservation of linear and angular momentum. Atwood machine, Virial Theorem, Non-conservative forces. Motion of Particles und... spherical shell. Parallel and perpendicular axis theorem, Degrees of freedom, instantaneous axis and cente
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad
- mensional spaces, F. Riesz Lemma, the Hahn-Banach theorem, the HB theorem for complex spaces, The HB theorem for normed spaces, the open mapping theorem, the closed graph theorem, uniform boundedness principle and i
- Measure Theory Handwritten Notes by Asim Marwat
- Tchebeshev's Inequality * Monotone Convergence Theorem * Fatou's Lema * Lebesgue Dominated Convergence Theorem for Non-negative Measurable Function * Convergence Theorem * Monoton Convergence Theorem * Lebesgue Dominated Convergence Theorem * Lebesgue Bounded Convergenc
- Ring (Notes) by Prof. M. Dabeer Mughal
- of ring, Boolean ring * Sub-ring and related theorem * Centre of ring and related theorem * Ring homomorphism * Isomorphism, kernel of $\phi$ and rela... Principal ideal, principal ideal ring and related theorem * Quotient ring and related theorem * Ist fundamental theorem * Maximal ideal and related theorem
- Group Theory by Mr. Muhammad Iftikhar
- * Cosets * Equivalence relation * Lagrange's theorem * Relation between groups * Homomorphism * Cayley's theorem * Conjugacy relation in groups * Conjugacy cl... actor group or quotient group * The isomorphism theorem * First isomorphism theorem * Second isomorphism theorem * Third isomorphism theorem * Automorphis
- Rings & Modules by Ms. Iqra Liaqat
- * Ring homomorphism * Quotient Module * First theorem of homomorphism * Second isomorphism theorem * Fundamental theorem of homomorphism * Internal direct sum * External direct sum * Finitely gener... polynomial * Constant polynomial * Remainder theorem * Zeros of the polynomial * Roots of the equa
- Affine and Euclidean Geometry by Shahzad Idress
- f Cosine and Sines: The Law of Cosine, Pythagoras Theorem, Parallelogram Law, The Law of Sines, * Eucl... 𝑩, Angles Associated with Parallel Lines, Thales’ Theorem, Menelaus Point, Menelaus’ Theorem, Cevian Line, Ceva’s Theorem, Copolar Triangles, Coaxial Triangles, Desargues’ Theorem. * Platonic Polyh