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Why have they not called in the National Guard?
EDIT: and why has it not simply been sent in without being asked for?

I'm not sure on what you mean by being "asked for". The national guard is under the command of the governor in each state. It is up to him/her to order the deployment. In general, it is good practice to see if local law enforcement can handle a situation before you begin deploying soldiers. That probably means that the governor was meeting with law enforcement and city officials to monitor the situation and make a determination of the capacity to restore peace through civilian instead of military means. Once they decided it was not possible, the governor ordered the deployment. Anyone that was in front of the media "asking" for the national guard to be deployed were probably not a part of that decision-making structure which was operating concurrently.

Certainly you understand that a mayor (or anyone, really) can request that the governor send them in. I didn't see or hear about any of that. It doesn't have to be done in front of a camera, but if it happened it would have been reported that the mayor had requested that the governor send them in...at least that's how it usually happens.

Have they been deployed now? They had not been last night, the last I saw. I can't understand how the city on fire, cops on the run and injured, and thousands of destructive looters on the streets doesn't meet the requirements, that happened early on. Instead of doing something, they announced a curfew for the next (5?) days and basically let the rioters do their thing on day one. Anyone injured is going to have a good case against the police/city/state for not taking action to stop it.
EDIT: I see now, they sent in 160 national guard members this morning (Tuesday) with more to come...zero on Monday or Monday night/Tuesday early morning.

When it's obvious that local law enforcement is outnumbered 10 to 1 or worse, and the "protestors" have become violent rioters attacking police, citizens, cars, and businesses, and lighting buildings and cars on fire, it's time. That was 3pm, and came with plenty of warnings online. There was pretty good indication that there would be exactly that problem, they should have had serious backup at the ready, they did not.

I can't fathom why there wasn't a curfew last night, there was plenty of time to see it was needed. I also can't fathom why the national guard wasn't requested (yes, I'm sticking with that being proper and normal, but not necessary) by the mayor, or why it wasn't sent in by the governor or the fed without being requested.

It really seemed the authorities could have foreseen there would be severe problems (they've been claiming they have serious credible death threats against the entire police force by numerous factions...that's enough right there to call/send in the National Guard yesterday, before the funeral). Waiting for the problems to happen, then allowing it to continue over night is shirking their duty because they're scared, IMO.

EDIT:from http://www.wsj.com/articles/national-guard-deployed-in-baltimore-amid-riots-after-freddie-grays-funeral-1430218096
Protests over Mr. Gray’s death had been largely peaceful until Saturday, when pockets of violence led to 35 arrests and caused minor injuries to six police officers.
Mr. Batts, the police commissioner, said late Monday that 250 to 300 officers assembled in West Baltimore after a social-media message called on high-school students Monday to stage a “purge”—an anarchic protest based on a film called “The Purge” that includes a period of lawlessness—at 3 p.m. starting at the Mondawmin Mall and ending downtown.
Baltimore police also said they received a threat that city gangs would join together to “take down” law-enforcement officers.

Police say a lot of things. What some gang members had to say.
http://www.wbaltv.com/news/gang-members-we-did-not-make-truce-to-harm-cops/32609810

I certainly think parents bear some responsibility for raising their kids to think this kind of behavior is acceptable.

Bunch of damn cockroaches that need to be dealt with.