Below you will find example sentences with "weak topology". The examples show how this phrase is used in real sentences and which words often surround it.

Weak Topology in a sentence

About this phrase

  • Belongs to the word: weak

Words in this phrase

weak

Meanings of words in this phrase

  • weak can mean: Lacking in force (usually strength) or ability. Frequent word

Context words

These words often appear near this phrase in the example sentences:

set 3× metrizable 3× coarsest 2× polar 2× original 2× functions 2× unit 2× ball 2× view 1× see 1× details 1× order 1×

Related phrases

too weak

Other phrases with this word

Other phrases with weak:

too weak 9×

Example types with weak topology

Below, the examples are grouped by length and sentence type:

Short example sentences

The weak topology is always metrizable. (6 words)

Other properties By definition, the weak* topology is weaker than the weak topology on X*. (15 words)

If the dual X ′ is separable, the weak topology of the unit ball of X is metrizable. (17 words)

Longer example sentences

If in addition, X* separates points on X (which means that for each x ∈ X there is a linear functional in X* that's non-zero on x ) then X with this weak topology becomes Hausdorff. (36 words)

W ; Weak topology : The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous. (35 words)

In order to distinguish the weak topology from the original topology on X, the original topology is often called the strong topology. (22 words)

Example sentences (8)

From this point of view, the weak topology is the coarsest polar topology ; see weak topology (polar topology) for details.

In order to distinguish the weak topology from the original topology on X, the original topology is often called the strong topology.

W ; Weak topology : The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous.

Other properties By definition, the weak* topology is weaker than the weak topology on X*.

Although the weak topology of the unit ball is not metrizable in general, one can characterize weak compactness using sequences.

If in addition, X* separates points on X (which means that for each x ∈ X there is a linear functional in X* that's non-zero on x ) then X with this weak topology becomes Hausdorff.

If the dual X ′ is separable, the weak topology of the unit ball of X is metrizable.

The weak topology is always metrizable.