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

Weak Topology in a sentence

Corpus data

  • Displayed example sentences: 8
  • Discovered as a combination around: weak
  • Corpus frequency in the collocation scan: 7
  • Phrase length: 2 words
  • Average sentence length: 21.4 words

Words in this phrase

weak topology

Meanings of words in this phrase

  • weak can mean: Lacking in force (usually strength) or ability. Frequent word
  • topology can mean: The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by conti... Less frequent word

Sentence profile

  • Phrase position: 4 start, 2 middle, 2 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

although the weak topology of the 1× definition the weak topology is weaker 1× distinguish the weak topology from the 1× separable the weak topology of the 1× than the weak topology on x 1× the weak topology is always 1× topology see weak topology polar topology 1× topology the weak topology on a 1×

Sentence openings and endings

Common sentence openings:

although the weak 1× if in addition 1× if the dual 1× in order to 1× other properties by 1× the weak topology 1×

Common sentence endings:

compactness using sequences 1× is always metrizable 1× the functions continuous 1× the strong topology 1× topology becomes hausdorff 1× topology for details 1×

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

Phrases around this combination

Other phrases discovered around weak:

too weak 9×

Just before it in the phrase index:

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Just after it in the phrase index:

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Corpus analysis

  • The phrase "weak topology" has 2 words and usually appears near the start in these examples. The average sentence has 21.4 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as although the weak topology of the, definition the weak topology is weaker, set, metrizable and coarsest stand out.
  • In the phrase index, this combination connects with too weak and too weak, linking the page to nearby combinations.

Example types with weak topology

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

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.