, ▁and ▁the ▁time ▁through ▁which ▁various ▁events ▁take ▁place . ▁The ▁expansion ▁of ▁space ▁is ▁in ▁reference ▁to ▁this ▁ 3 - D ▁manifold ▁only ; ▁that ▁is , ▁the ▁description ▁involves ▁no ▁structures ▁such ▁as ▁extra ▁dimensions ▁or ▁an ▁exterior ▁universe . ▁ ▁The ▁ult imate ▁topology ▁of ▁space ▁is ▁a ▁posterior i ▁– ▁something ▁which ▁in ▁principle ▁must ▁be ▁observed ▁– ▁as ▁there ▁are ▁no ▁constraints ▁that ▁can ▁simply ▁be ▁reason ed ▁out ▁( in ▁other ▁words ▁there ▁can ▁not ▁be ▁any ▁a ▁pri ori ▁constraints ) ▁on ▁how ▁the ▁space ▁in ▁which ▁we ▁live ▁is ▁connected ▁or ▁whether ▁it ▁wra ps ▁around ▁on ▁itself ▁as ▁a ▁compact ▁space . ▁Though ▁certain ▁cosm ological ▁models ▁such ▁as ▁Gö del ' s ▁universe ▁even ▁permit ▁b izar re ▁world lines ▁which ▁intersect ▁with ▁themselves , ▁ultimately ▁the ▁question ▁as ▁to ▁whether ▁we ▁are ▁in ▁something ▁like ▁a ▁" P ac - Man ▁universe " ▁where ▁if ▁travel ing ▁far ▁enough ▁in ▁one ▁direction ▁would ▁allow ▁one ▁to ▁simply ▁end ▁up ▁back ▁in ▁the ▁same ▁place ▁like ▁going ▁all ▁the ▁way ▁around ▁the ▁surface ▁of ▁a ▁bal lo on ▁( or ▁a ▁planet ▁like ▁the ▁Earth ) ▁is ▁an ▁observ ational ▁question ▁which ▁is ▁const rained ▁as ▁meas urable ▁or ▁non - me as urable ▁by ▁the ▁universe ' s ▁global ▁geometry . ▁At ▁present , ▁observations ▁are ▁consistent ▁with ▁the ▁universe ▁being ▁infinite ▁in ▁extent ▁and ▁simply ▁connected , ▁though ▁we ▁are ▁limited ▁in ▁distingu ishing ▁between ▁simple ▁and ▁more ▁complicated