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Explore Clopen through 5 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

Rare word

Clopen in a sentence

Clopen meaning

Both open and closed.

Using Clopen

  • The main meaning on this page is: Both open and closed.
  • In the example corpus, clopen often appears in combinations such as: closed clopen, clopen set, clopen sets.

Context around Clopen

  • Average sentence length in these examples: 19 words
  • Position in the sentence: 0 start, 2 middle, 3 end
  • Sentence types: 5 statements, 0 questions, 0 exclamations

Often before:

closed 1×

Often after:

set 2× sets 2×

Sentence patterns with Clopen

These short patterns come directly from the example sentences and show how the word is often embedded:

and closed clopen 1× closed a clopen set 1× closed both clopen set or 1× of all clopen sets containing 1× the only clopen sets are 1×

Sentence openings and endings

Common sentence openings:

a set may 1× a subset of 1× equivalently a space 1× hence in any 1× let be the 1×

Common sentence endings:

a clopen set 1× and closed clopen 1× or locally connected 1× set or neither 1× the empty set 1×

Words around Clopen

Just before it in the word index:

clop 13 clooneys 6 clooney 192 cloonan 2 clontz 5 clontarf 18

Just after it in the word index:

clopidogrel 3 clops 2 clopton 7 cloquet 22 clore 3 cloridectomy 2

Similar in corpus frequency:

aaas 7 aacc 7 aacs 7 aafes 7 aah 7 aankh 7

Corpus analysis for Clopen

  • In this selection, "clopen" usually appears near the end of the sentence. The average example has 19 words, and this corpus slice is mostly made up of statements.
  • Around the word, closed, set and sets stand out and add context to how "clopen" is used.
  • Recognizable usage signals include and closed clopen and closed a clopen set. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "clopen" sits close to words such as aaas, aacc and aacs, which helps place it inside the broader word index.

Example types with clopen

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

A set may be both open and closed (a clopen set ). (11 words)

A subset of X may be open, closed, both ( clopen set ), or neither. (13 words)

Hence, in any topology, the entire space is simultaneously open and closed (" clopen "). (13 words)

Longer example sentences

Let be the connected component of x in a topological space X, and be the intersection of all clopen sets containing x (called quasi-component of x.) Then where the equality holds if X is compact Hausdorff or locally connected. (40 words)

Equivalently, a space is connected if the only clopen sets are the whole space and the empty set. (18 words)

A subset of X may be open, closed, both ( clopen set ), or neither. (13 words)

Example sentences (5)

A set may be both open and closed (a clopen set ).

A subset of X may be open, closed, both ( clopen set ), or neither.

Equivalently, a space is connected if the only clopen sets are the whole space and the empty set.

Hence, in any topology, the entire space is simultaneously open and closed (" clopen ").

Let be the connected component of x in a topological space X, and be the intersection of all clopen sets containing x (called quasi-component of x.) Then where the equality holds if X is compact Hausdorff or locally connected.

Common combinations with clopen

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "clopen" in a sentence?
An example: "A set may be both open and closed (a clopen set )." This page contains 5 example sentences with the word "clopen" from authentic English texts.
What does "clopen" mean?
Clopen means: Both open and closed.
How many example sentences with "clopen" are there?
Voorbeeldzinnen.info contains 5 example sentences with "clopen", drawn from a database of millions of English sentences.