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On semilocally simply connected spaces
Fischer, Hanspeter ...
Namen tega članka je: (i) opisati prostor, ki ustreza Spanierjevi definiciji šibke lokalne enostavne povezanosti, čeprav je njegova Spanierjeva grupa netrivialna; (ii) predlagati spremembo pojma ...Spanierjeve grupe tako, da bo ta karakterizirala šibko lokalno enostavno povezanost; (iii) dokazati, da rahlo spremenjena definicija šibke lokalne enostavne povezanosti, ki se ponekod pojavlja v literaturi, ustreza standardni karakterizaciji s Spanierjevo grupo v kategoriji s potmi povezanih prostorov. Lastnost šibke lokalne enostavne povezanosti ima ključno vlogo v klasični teoriji krovnih prostorov. V posplošeni teoriji krovnih prostorov enakovredno vlogo igrajo homotopsko Hausdorffova lastnost in njene izpeljave. Članek med drugim obravnava povezave med dotičnimi lastnostmi in uporabi Spanierjevo grupo za dokaz najšibkejše algebraične karakterizacije obstoja posplošenih krovnih prostorov v smislu Fischerja in Zastrowa. Neobrnljivost večino dokazanih implikacij se dokaže s protiprimeri, med katerimi so nekateri predstavljeni prvič.
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