In flight, we get warnings when changing airspace, we can touch the screen and check what airspace we are in that is very good.
B‌ut I propose to have a permanent box (like GS, DST NXT) where the current airspace is always displayed. This would be an additional safety against airspace violations.
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‌Airspace vertical limits are specified  ASL, AGL or FL.
GPS altitude and terrain data should be ok for ASL and AGL, that is usually  the low level complex airspace that is the most difficult to figure out.
F‌or the less complex higher level airspace defined by FL, local QNH (or static pressure) would unfortunately be needed for an accurate indication.