Five Points, just a few blocks north of the state capitol, is a historically black neighborhood that was once so full of jazz musicians that it was called the Harlem of the West.

Today, a portion of Five Points has been rebranded River North (RiNo, for those in the know) and has become fashionable with young professionals. The area has come to symbolize rapid growth and redevelopment in Denver, much as the Williamsburg neighborhood became the face of transformation in Brooklyn.

On the industrial side of the neighborhood, the streets that are not already lined with new breweries, cannabis shops and condominiums are alive with cranes and jackhammers. On the adjacent residential streets, many longtime residents, including most of Ms. Wright’s childhood neighbors, have been priced out of their bungalows.

A thousand families a month are moving to Denver these days, and the exploding demand for housing has pushed up rents and property values. The median price of a single-family home has doubled in the last five years, to about $450,000. That price is beyond the reach of about half the city’s residents, according to researchers at Harvard University.

Though the city’s population is overwhelmingly white, it has a black mayor and a black City Council president. Community organizers have been calling on city officials to take a more aggressive approach to creating and protecting affordable housing, pointing out that minority residents are more likely to be displaced by rising rents.

Ink’s sidewalk sign, created for the coffee shop by an advertising agency, appeared just before Thanksgiving on a retail strip full of new bars and boutiques. The message on the back extended the theme, and for some, rubbed salt in the wound: “Nothing says gentrification like being able to order a cortado.”