## Base or Open Base of a Topology

Let be a topological space, then the sub collection of is said to be a base or bases or open... Click here to read more

From basic to higher mathematics

Let be a topological space, then the sub collection of is said to be a base or bases or open... Click here to read more

Let be a topological space. A sub-collection of subsets of is said to be an open subbase for or a... Click here to read more

Let be a topological space and , then the sub collection is said to be local bases at a point... Click here to read more

Let be a topological space, then is said to be the first countable space if for every has a countable... Click here to read more

Let be a topological space, then is said to be the second countable space, if has a countable base. In... Click here to read more

Open Cover Let be a topological space. A collection of open subsets of is said to be an open cover... Click here to read more

A topological space is said to be a separable space if it has a countable dense subset in ; i.e.,... Click here to read more

Let be a function defined from topological space to topological space , then is said to be continuous at a... Click here to read more

Open Mapping A mapping from one topological space into another topological space is said to be an open mapping if... Click here to read more

A function is said to be a homeomorphism (topological mapping) if and only if the following conditions are satisfied: (1)... Click here to read more

A property is said to be a topological property if whenever a space has the property , all spaces which... Click here to read more

Products of Sets If and are two non-empty sets, then the Cartesian product is defined as . Projection Maps... Click here to read more