Description
The include option for the sdk/include has an extra slash between those two directory names. Below is the compile command for my test sketch file (extra EOLs added for readability). The double slash is in the third line.
C:\Users\Don\AppData\Roaming\Arduino15\packages\esp8266\tools\xtensa-lx106-elf-gcc\1.20.0-26-gb404fb9/bin/xtensa-lx106-elf-g++
-D__ets__ -DICACHE_FLASH -U__STRICT_ANSI__
-IC:\Users\Don\AppData\Roaming\Arduino15\packages\esp8266\hardware\esp8266\1.6.5-947-g39819f0/tools/sdk//include
-c -Os -g -mlongcalls -mtext-section-literals -fno-exceptions -fno-rtti -falign-functions=4 -std=c++11
-MMD -DF_CPU=80000000L -DARDUINO=10605 -DARDUINO_ESP8266_THING -DARDUINO_ARCH_ESP8266 -DESP8266
-IC:\Users\Don\AppData\Roaming\Arduino15\packages\esp8266\hardware\esp8266\1.6.5-947-g39819f0\cores\esp8266
-IC:\Users\Don\AppData\Roaming\Arduino15\packages\esp8266\hardware\esp8266\1.6.5-947-g39819f0\variants\thing
C:\Users\Don\AppData\Local\Temp\build1303870529194311090.tmp\sketch_aug26b.cpp
-o C:\Users\Don\AppData\Local\Temp\build1303870529194311090.tmp\sketch_aug26b.cpp.o