![]() ![]() "sourceName": "StarCitizen_Explore_Crop", "sourceUrl": "/i/1b1acdbe5aeef180f0139d8669f7d64d7de0a775/ADdPNihJzmPbNuTnFsH1DqUeqBRpXdSXVVtgJTyDDgscGKrzJuoFjResj64bzE8C79rzJPbiF78nUmiHrjxftL2xe/50/starcitizen-explore-crop.jpg" "max": "/i/bcfc972d56068cae20945cc80fe51619f9e77980/ADdPNihJzmPbNuTnFsH1DqUeqBRpXdSXVVtgJTyDDgscGKrzJuoFjResj64bzE8C79rzJPbiF78nUmiHrjxftL2xe/starcitizen-explore-crop.webp", "max": "/i/bcfc972d56068cae20945cc80fe51619f9e77980/ADdPNihJzmPbNuTnFsH1DqUeqBRpXdSXVVtgJTyDDgscGKrzJuoFjResj64bzE8C79rzJPbiF78nUmiHrjxftL2xe/starcitizen-explore-crop.jpg", Whether it's a hidden outpost, a derelict ship or a beautiful sunset, explorers are eager to see what's waiting over that next ridge.", They will seek out the unknown or sometimes just surrender to the thrill of getting lost. The explorer builds a life on the pursuit of knowledge and discovery. With unmatched beauty, diversity, and danger in equal measure, you never know what’s waiting for you when you take flight.", Star Citizen gives you unlimited run of the Stanton system, a vast sandbox of life-size planets, moons, cities, space stations, asteroid belts, and more. And, if you look hard enough, Stanton’s booming black market offers opportunities to earn a crooked living if a hard day’s work isn’t for you. Hauling cargo, mining ore, salvaging wrecks, hunting criminal bounties – there’s a career to suit everyone. ![]() The infinite join is just the colimit of the inclusions $G\to G*G\to G*G*G\to\dots$, and each of these inclusions is nullhomotopic, so the colimit is contractible.įor intuition, the example $G=\mathbb$, and in the limit you get the infinite sphere $S^\infty$ which is contractible.The Stanton system has a thriving economy based around immersive careers that you can dip into or fully embrace. ![]() Note that if $X$ is any space and $Y$ is any nonempty space, then the inclusion $X\to X*Y$ is nullhomotopic (any point of $Y$ gives a cone over $X$ in $X*Y$). (See the comments at Connectedness of the join of two spaces for a sketch of one way to prove this fact.) It follows by induction that the $n$-fold join $G*G*\dots*G$ is $(n-2)$-connected for all $n$ and so the infinite join is contractible.Īlternatively, here is an easier argument. As the argument says, you can justify this using the fact that joins increase connectivity: if $X$ is $n$-connected and $Y$ is $m$-connected then $X*Y$ is $(n m 1)$-connected. The claim is that the infinite join $G*G*G*\dots$ is contractible, so your example with $G*G$ is irrelevant. ![]()
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