Topological Spaces

Let $$X$$ be a non empty set. A collection $$\tau $$ of subsets of $$X$$ is said to be a… Click here to read more

If $${\tau _1}$$ and $${\tau _2}$$ are two topologies defined on the non empty set X such that $${\tau _1}… Click here to read more

Indiscrete Topology The collection of the non empty set and the set X itself is always a topology on X,… Click here to read more

The intersection of any two topologies on a non empty set is always topology on that set, while the union… Click here to read more

Usual Topology on $$\mathbb{R}$$ A collection of subsets of $$\mathbb{R}$$ which can be can be expressed as a union of… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space, then a member of $$\tau $$ is said to be an… Click here to read more

Let $$X$$ be a non empty set, and then the collection of subsets of $$X$$ whose compliments are finite along… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space, then a subset of X whose complement is a member of… Click here to read more

We shall describe a method of constructing new topologies from the given ones. If $$\left( {X,\tau } \right)$$ is a… Click here to read more

Let $$X$$ be a topological space with topology $$\tau $$, and $$A$$ be a subset of $$X$$. A point $$x… Click here to read more

Let $$A$$ be a subset of a topological space $$X$$, then a point $$x \in A$$ is said to be… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space and $$A$$ be a subset of $$X$$, then the closure of… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space. A subset $$N$$ of $$X$$ containing $$x \in X$$ is said… Click here to read more

Let $$\left( {X,\tau } \right)$$ be the topological space and $$A \subseteq X$$, then a point $$x \in A$$ is… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space and $$A$$ be a subset of $$X$$, then a point $$x… Click here to read more

Let $$A$$ be a subset of a topological space $$X$$, a point $$x \in X$$ is said to be boundary… Click here to read more