1. The Texas Declaration of Independence was adopted on June 4, 1836, officially declaring Texas as a republic independent from Mexico. This was a significant moment in Texas history, leading to the eventual annexation of Texas by the United States in 1845.

2. On June 4, 1924, the Alpha Kappa Alpha sorority was founded at Howard University in Washington, D.C. This sorority is notable for being the first Black Greek letter organization for women, and it has since become a prominent institution in the African American community.

3. The Texas Department of Public Safety was established on June 4, 1935, as a merger between the Texas Rangers and the Texas Highway Patrol. This agency is responsible for law enforcement and public safety in the state of Texas, including issuing driver's licenses and conducting criminal investigations.

4. On June 4, 1961, Texas astronaut Edward Higgins White II became the first American to walk in space during the Gemini 4 mission. This historic event marked a significant milestone in space exploration and paved the way for future spacewalks and missions.

5. The Houston Rockets won their first NBA championship on June 4, 1994, defeating the New York Knicks in game seven of the finals. This victory was a significant moment in Texas sports history, and the Rockets went on to win another championship in 1995.