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There are several options to obtain the needed extensions to get WiFi working.
The easiest is to connect the RPi with an Ethernet cable to Internet.
You can than use `tce-load -wi <extension-name>` to install them.
Below the steps to first download the needed extensions to an USB-stick and install them from there.
The needed files depend on the type of RPi and if you have a 32-bit (armhf) or 64-bit (aarch64) piCore OS.
http://repo.tinycorelinux.net/15.x/aarch64/tcz/firmware-rpi-wifi.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/firmware-rpi-wifi.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/wpa_supplicant.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/wpa_supplicant.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/wpa_supplicant.tcz.dep http://repo.tinycorelinux.net/15.x/aarch64/tcz/readline.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/readline.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/readline.tcz.dep http://repo.tinycorelinux.net/15.x/aarch64/tcz/libnl.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/libnl.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/ncurses.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/ncurses.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/wifi.tcz http://repo.tinycorelinux.net/15.x/aarch64/tcz/wifi.tcz.md5.txt http://repo.tinycorelinux.net/15.x/aarch64/tcz/wifi.tcz.dep
tce-load -i firmware-rpi-wifi.tcz tce-load -i wifi.tcz tce-load -i wireless-6.6.47-piCore-v7.tcz tce-load -i wireless_tools.tcz tce-load -i wpa_supplicant.tcz
firmware-rpi-wifi.tcz wifi.tcz wireless_tools.tcz wpa_supplicant.tcz
etc/wpa_supplicant.conf
wifi.sh -a &> /home/tc/wifi.log &