# What is meant by second countable?

## What is meant by second countable?

From Wikipedia, the free encyclopedia. In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.

### What is a separable topology?

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence. of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

#### Is every second-countable space Metrizable?

Every second countable regular space is metrizable. While every metrizable space is normal (and regular) such spaces do not need to be second countable. For example, any discrete space X is metrizable, but if X consists of uncountably many points it does not have a countable basis (Exercise 4.10).

**What is a second countable topological space?**

Definition. In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.

**What is separable function?**

Introduction. A function of 2 independent variables is said to be separable if it can be expressed as a product of 2 functions, each of them depending on only one variable.

## Is separability a hereditary property?

3. Separability and ccc are not hereditary. To show this, we need a separa- ble/ccc topological space with a subspace that is not separable/ccc.

### Are all functions separable?

Note that constant functions like F(x, y) = 5 or functions of one variable F(x, y) = h(y) are additively separable. But not all functions are additively separable, later we will see F(x, y) = xy is not additively separable.

#### What is a separable graph?

A graph. is said to be separable if it is either disconnected or can be disconnected by removing one vertex, called articulation. A graph that is not separable is said to be biconnected (or nonseparable). SEE ALSO: Articulation Vertex, Biconnected Graph, Quasiseparable Graph.

**Is property of compactness hereditary?**

In topology Sequentiality and Hausdorff compactness are weakly hereditary, but not hereditary.

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