What occur s when a layer of warm air traps a layer of cold air?

This is a good question, and there are a few things going on here.

First, smog is not really related to CO2. There are other pollutants produced by burning fossil fuels, mainly sulfur dioxide and Ozone that produce the hazy conditions and respiratory damage associated with smog.

However, it is true that the especially high levels of smog in places like LA and Mexico City result from gases produced in the city being trapped at low altitudes. This occurs because of a phenomenon called a temperature inversion. Usually, air decreases in temperature as it rises, and cooler air is less dense, so it rises. So polluted air near the ground in a city is gets warmed (because the ground is warmer than the air) and it rises. As it rises, it cools off and tends to keep rising up into the upper atmosphere. A temperature inversion occurs when air near the ground is relatively cool, and there is a layer of warmer air above it. That upper layer of warm air keeps the cooler air from rising, and traps all of the pollution in the cooler, lower layer. So for example in LA, you tend to have relatively cool air near the ground because of sea breezes from the nearby ocean. But you also tend to have warmer air coming over the mountains from the desert (think of the warm Sundowners and Santa Ana winds as extreme examples of this). That layer of warm air traps the cool, polluted air in the city. Similar things can happen in deep mountain valleys (like where Mexico City is) because the valley floor gets very cold at night and the cold air then gets trapped in the valley.

OK, so CO2 and other gases can get trapped near the ground in LA. How does that relate to global warming? Well, for one thing, that sort of temperature inversion only occurs in certain geographic locations. So in most places around the world, there is nothing stopping CO2 from rising into the atmosphere and entering global circulation. Only a small fraction of man-made CO2 is produces in LA, so that effect is pretty small on a global scale. Second, it turns out that LA is not smoggy 365 days a year. Under some weather patterns the inversion lifts and all of the air trapped near the ground rises into the upper atmosphere. So while the inversion might trap CO2 temporarily, it does not permanently prevent that CO2 from entering the upper atmosphere.

Carbon dioxide is not really part of smog. Smog is a result of different pollutants in the air, most of which come from the burning of fossil fuels. These chemicals can react with each other, often by reactions that involve sunlight, to produce things like ozone,nitrogen oxides, and various organic (carbon-containing) that are the major components of smog. It is true that when a city is surrounded by mountains, the air does not circulate as much, so smog can build up to higher levels. High levels of smog are also typically associated with events called temperature inversions. Normally, the air is cooler as you go higher up in the troposphere, the lowest layer of the atmosphere (it goes from the surface to about 5 to 10 miles above the surface). This is because the Sun's rays heat up the surface of the Earth, which in turn heats up the air immediately over the surface;when air is heated, it expands and rises (just like a hot-air balloon), and cold air will fall down to take its place, all of which results in air circulation and consequently the removal of pollutants from areas near the surface. During a temperature inversion, however,air temperature will stay constant or even increase as you go higher up, making it harder for air near the surface to become light enough to be able to rise very far, so the air will stagnate and smog can build up. Los Angeles is susceptible to temperature to inversions because at the surface there is often cold air that flowed over the oceans, while global air circulation results in a warmer layer above this.

So the bottom line is that smog builds up in cities due to temporary circumstances that cause atmospheric circulation to be reduced.Eventually, however, the air in the cities will become mixed with the rest of the atmosphere. We know that levels of carbon dioxide in the atmosphere are increasing because we can measure it directly--today the concentration of carbon dioxide is about 385 parts per million,while prior to the Industrial Revolution, when extensive burning of fossil fuels began, the concentration was something like 280 parts permillion

It is ozone and particulate matter, not carbon dioxide, that compose smog. The production of smog does also generate carbon dioxide, but the global greenhouse effect does not take place in the same way nor for the same reason as health damage from local air pollution.