Editing Glossary of general topology (section)

== I ==

; Identification map: See '''[[Quotient map (topology)|Quotient map]]'''.
; [[Quotient space (topology)|Identification space]]: See '''[[Quotient space (topology)|Quotient space]]'''.
; [[Indiscrete space]]: See '''[[Trivial topology]]'''.
; [[Infinite-dimensional topology]]: See '''[[Hilbert manifold]]''' and '''[[Q-manifolds]]''', i.e. (generalized) manifolds modelled on the Hilbert space and on the Hilbert cube respectively.
; Inner limiting set: A ''G''<sub>δ</sub> set.<ref name=ss162/>
; [[Interior (topology)|Interior]]: The [[interior (topology)|interior]] of a set is the largest open set contained in the original set. It is equal to the union of all open sets contained in it. An element of the interior of a set ''S'' is an '''interior point''' of ''S''.
; Interior point: See '''[[Interior (topology)|Interior]]'''.
; [[Isolated point]]: A point ''x'' is an [[isolated point]] if the [[singleton (mathematics)|singleton]] {''x''} is open. More generally, if ''S'' is a subset of a space ''X'', and if ''x'' is a point of ''S'', then ''x'' is an isolated point of ''S'' if {''x''} is open in the subspace topology on ''S''.
; Isometric isomorphism: If ''M''<sub>1</sub> and ''M''<sub>2</sub> are metric spaces, an isometric isomorphism from ''M''<sub>1</sub> to ''M''<sub>2</sub> is a [[bijection|bijective]] isometry ''f'' : ''M''<sub>1</sub> &nbsp;→&nbsp; ''M''<sub>2</sub>. The metric spaces are then said to be '''isometrically isomorphic'''. From the standpoint of metric space theory, isometrically isomorphic spaces are identical.
; Isometry: If (''M''<sub>1</sub>, ''d''<sub>1</sub>) and (''M''<sub>2</sub>, ''d''<sub>2</sub>) are metric spaces, an isometry from ''M''<sub>1</sub> to ''M''<sub>2</sub> is a function ''f'' : ''M''<sub>1</sub> &nbsp;→&nbsp; ''M''<sub>2</sub> such that ''d''<sub>2</sub>(''f''(''x''), ''f''(''y'')) = ''d''<sub>1</sub>(''x'', ''y'') for all ''x'', ''y'' in ''M''<sub>1</sub>. Every isometry is [[Injective function|injective]], although not every isometry is [[surjection|surjective]].