nLab analysis - contents

analysis (differential/integral calculus, functional analysis, topology)

epsilontic analysis

infinitesimal analysis

computable analysis

Introduction

Basic concepts

triangle inequality

metric space, normed vector space

open ball, open subset, neighbourhood

metric topology

sequence, net

convergence, limit of a sequence

compactness, sequential compactness

differentiation, integration

topological vector space

Basic facts

continuous metric space valued function on compact metric space is uniformly continuous

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Theorems

intermediate value theorem

extreme value theorem

Heine-Borel theorem

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