Graduate Quotient maps, group action, open maps

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The discussion centers on proving that the quotient map p: X → X/G is open when a topological group G acts continuously on a topological space X. The participants explore the implications of the continuity of the group action, specifically how open sets in X transform under this action. They establish that for any open neighborhood U in X, the set g.U is also open, leveraging the continuity of the left multiplication map l_g. The conversation highlights the necessity of understanding group actions and their properties in topology, concluding that the group action guarantees the openness of the quotient map. This foundational concept is crucial for further exploration in topology and group theory.
  • #31
Ok, thank you
 
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  • #32
I think I saw this and someone thought it was homework. A bit ambitious homework if you ask me, but o.k., a mentor (not me) thought so. Try it again in the homework section or contact the mentor who classified it as homework.
 
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