Store values in library

So are library H files delared in glabal scope?

After you mentioned Serial.begin() which is a good example, I found the Serial reference in C:\Program Files (x86)\Arduino\hardware\arduino\cores\arduino Below is the snipplet of code that I found relevant to Serial.

#include "HardwareSerial.h"

uint16_t makeWord(uint16_t w);
uint16_t makeWord(byte h, byte l);

#define word(...) makeWord(__VA_ARGS__)

unsigned long pulseIn(uint8_t pin, uint8_t state, unsigned long timeout = 1000000L);

void tone(uint8_t _pin, unsigned int frequency, unsigned long duration = 0);
void noTone(uint8_t _pin);

// WMath prototypes
long random(long);
long random(long, long);
void randomSeed(unsigned int);
long map(long, long, long, long, long);

#endif

#include "pins_arduino.h"

#endif

So can I declare a global variable in the H file of the library that will be stored automatically within the global scoop when I use the library?