It is well known that the topology is a major branch of mathematics which has several applications to many other branches. I just want to have an answer to such question which is near to the real life.
Perhapes you are not acquainted with Mobius strip. There are two ways by which Topology is read Algebraic Topology and geometrical Topology. Algebraic Topology is used in Computer application and Geometrical Topology is used in space for data analysis.
I don't know what are you meaning by applications of real life. One of the most fashionable branches in Condensed Matter nowadays are the Topological Materials as the Topological Insulators, Weyl semimetals or Quantized Majorana Conductivity. These phenomena are open new perspectives in Topological Quantum Computing or to understand properly how the Thermoelectricity has good efficience or not.