Bases and Subbases

Let $$\left( {X,\tau } \right)$$ be a topological space, then the sub collection $${\rm B} $$ of $$\tau $$ is… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space. A sub-collection $$S$$ of subsets of $$X$$ is said to be… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space and $$x \in X$$, then the sub collection $${{\rm B}_x}$$ is… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space, then $$X$$ is said to be the first countable space if… Click here to read more

Let $$\left( {X,\tau } \right)$$ be a topological space, then $$X$$ is said to be the second countable space, if… Click here to read more

Open Cover Let $$\left( {X,\tau } \right)$$ be a topological space. A collection $$\left\{ {{U_\alpha }:\alpha \in I} \right\}$$ of… Click here to read more

A topological space $$\left( {X,\tau } \right)$$ is said to be a separable space if it has a countable dense… Click here to read more

Let $$f$$ be a function defined from topological space $$X$$ to topological space $$Y$$, then $$f$$ is said to be… Click here to read more

Open Mapping A mapping $$f$$ from one topological space $$X$$ into another topological space $$Y$$ is said to be an… Click here to read more

A function $$f:X \to Y$$ is said to be a homeomorphism (topological mapping) if and only if the following conditions… Click here to read more

A property $$P$$ is said to be a topological property if whenever a space $$X$$ has the property $$P$$, all… Click here to read more

Products of Sets If $${X_1}$$ and $${X_2}$$ are two non-empty sets, then the Cartesian product $${X_1} \times {X_2}$$ is defined… Click here to read more