# Topology subject

## Topology subjects

Topology $$\tau$$ has many concepts. In this post, I’ll summarize the concepts in topology.

Topology $$\tau$$ defines subsets that contains close elements. The closeness makes other properties related with subsets.

Topological space is a set defined with topology $$\tau$$.
-Matric topological space
-Cofinite topological space
-Subspace topology

#### Basis for a topology

Basis $$B$$ is a family set of subsets that construct topology $$\tau$$.

#### Closed set and limit points

Closed set is complement of open set.
Limit points of a open set A are all open set containing $$x$$ has other elements in $$A$$ except $$x$$.

#### Continuous function

Continuous function is defined in topological space.
A function is continuous if and only if $$f(A)$$ is open then $$f^{-1}(A)$$ is open.

#### Quotiont topology

Domain $$X$$, range $$Y$$ and function $$f$$. open set $$X$$, surjective function $$f:X \rightarrow Y$$, The $$quotient$$ $$topology$$ on Y (from $$X$$) is the collection of subset $$U \subset Y$$ such that $$f^{-1}(U)$$ is open in $$X$$