Editing Glossary of general topology (section)

== O ==

; [[Open cover]]: An [[open cover]] is a cover consisting of open sets.<ref name=ss163/>

; Open ball: If (''M'', ''d'') is a metric space, an open ball is a set of the form ''B''(''x''; ''r'') := {''y'' in ''M'' : ''d''(''x'', ''y'') < ''r''}, where ''x'' is in ''M'' and ''r'' is a [[positive number|positive]] [[real number]], the '''radius''' of the ball. An open ball of radius ''r'' is an '''open ''r''-ball'''. Every open ball is an open set in the topology on ''M'' induced by ''d''.
; Open condition:  See '''open property'''.
; [[Open set]]: An [[open set]] is a member of the topology.
; [[Open map|Open function]]: A function from one space to another is [[open map|open]] if the [[image (mathematics)|image]] of every open set is open.
; Open property:  A property of points in a [[topological space]] is said to be "open" if those points which possess it form an [[open set]].  Such conditions often take a common form, and that form can be said to be an ''open condition''; for example, in [[metric space]]s, one defines an open ball as above, and says that "strict inequality is an open condition".

;[[Orthocompact space|Orthocompact]]
: A space is orthocompact, if every [[open cover]] has an interior-preserving open [[Refinement (topology)|refinement]].