Text: we concentrate on some areas where the actual lattice structure of l plays a major part in a topological theory.

Correct capitalization: We concentrate on some areas where the actual lattice structure of L plays a major part in a topological theory.

Text: the richness these communities could bring to european society is often overlooked and tainted by stereotypes and prejudices.

Correct capitalization: The richness these communities could bring to European society is often overlooked and tainted by stereotypes and prejudices.

Text: let's look at some typical examples.

Correct capitalization: Let's look at some typical examples.

Text: mom, japanese, mature, japanese mom

Correct capitalization:
mom, Japanese, mature, Japanese mom