[[!redirects analysis]] [[!redirects Analysis in HoTT]] Here we collect articles about doing analysis in HoTT. ## General ## * [[directed type]] * [[net]] and [[sequence]] * [[preconvergence space]] * [[limit of a net]] * [[Hausdorff space]] * [[sequentially Hausdorff space]] ## Pointwise analysis ### * [[limit of a function]] * [[pointwise continuous function]] * [[function limit space]] ## Intervals ## * [[open interval]] * [[lower bounded open interval]] * [[upper bounded open interval]] * [[closed interval]] * [[unit interval]] * [[dyadic interval coalgebra]] * [[rational interval coalgebra]] * [[decimal interval coalgebra]] ## Differential calculus ## * [[function limit space]] * [[limit of a function]] * [[pointwise continuous function]] * [[algebraic limit field]] * [[limit of a binary function approaching a diagonal]] * [[difference quotient]] * [[differentiable function]] * [[Newton-Leibniz operator]] * [[derivative]] * [[inverse image]] * [[iterated inverse image]] * [[infinitely iterated inverse image]] * [[iterated differentiable function]] * [[smooth function]] * [[antiderivative]] * [[algebraic limit vector space]] * [[partial derivative]] * [[directionally differentiable function]] * [[directional derivative]] * [[calculus Clifford algebra]] * [[calculus geometric algebra]] * [[geometric derivative]] * [[uniformly continuous function]] ## Cauchy spaces ## * [[premetric space]] * [[Cauchy net]] * [[Cauchy approximation]] * [[modulus of Cauchy convergence]] * [[Cauchy structure]] * [[modulated Cauchy real numbers]] * [[HoTT book real numbers]] * [[Cauchy complete Archimedean ordered field]] ## Real analysis ## * [[real numbers]] * [[infinite decimal representation of a unit interval]] * [[pre-algebra real numbers]] * [[real unit interval]] * [[frame]] * [[locale]] * [[Dedekind cut]] * [[Dedekind real numbers]] * [[Dedekind cut structure]] * [[Dedekind cut structure real numbers]] * [[interval cut]] * [[Dedekind real closed intervals]] * [[sigma-frame]] * [[sigma-locale]] * [[Sierpinski space]] * [[localic real numbers]] * [[sigma-localic real numbers]] * [[MacNeille real numbers]] * [[Eudoxus real numbers]] * [[posite]] * [[ideal]] * [[filter]] * [[an axiomatization of the real numbers]] ## Functional analysis ## ... ## References ## * [[HoTT Book]]