Homeomorphism in a sentence
Synonym: mapping.
Meaning: A concept in topology where two shapes can be transformed into each other; significant in mathematics.
(1) Bilection is used to define homeomorphism.
(2) The concept of homeomorphism is fundamental in topology.
(3) The concept of a homeomorphism is fundamental in topology.
(4) A homeomorphism preserves the topological properties of a space.
(5) The idea of a homeomorphism can be extended to higher dimensions.
(6) A homeomorphism can transform a complicated space into a simpler one.
(7) A homeomorphism is a bijective mapping between two topological spaces.
(8) The concept of a homeomorphism is closely related to the notion of continuity.
(9) The concept of a homeomorphism is applicable to both finite and infinite spaces.
(10) An automorphism of a topological space is a homeomorphism from the space to itself.
Homeomorphism sentence
(11) The concept of homeomorphism is used in many fields, including physics and biology.
(12) The concept of a homeomorphism is applicable to both continuous and discrete spaces.
(13) The existence of a homeomorphism implies that two spaces are topologically equivalent.
(14) The properties of a homeomorphism can be studied using techniques from algebraic topology.
(15) The properties of a homeomorphism can be used to classify different types of geometric shapes.
(16) The existence of a homeomorphism between two spaces implies that they share certain properties.
(17) The concept of a homeomorphism is fundamental in understanding the structure of different spaces.
(18) The existence of a homeomorphism between two spaces can be proven using rigorous mathematical techniques.
(19) An automorphism can be thought of as a self-homeomorphism that preserves the topological properties of an object.
Homeomorphism meaning
Homeomorphism is a mathematical term that refers to a function between two topological spaces that preserves the structure of the spaces. In simpler terms, it is a way of transforming one space into another while maintaining its essential properties. If you are studying mathematics or any related field, you may come across this term and need to use it in your writing. Here are some tips on how to use the word homeomorphism in a sentence:
1. Understand the meaning of the word: Before using the word homeomorphism in a sentence, it is essential to understand its meaning. You should know that it is a mathematical term that refers to a function between two topological spaces that preserves the structure of the spaces.
2. Use it in a mathematical context: Homeomorphism is a term that is used in mathematics, so it is essential to use it in a mathematical context.
For example, you can say, "The two topological spaces are homeomorphic," or "The function is a homeomorphism."
3. Provide an example: To make your sentence more understandable, you can provide an example of homeomorphism. For instance, "The sphere and the torus are homeomorphic because they have the same number of holes."
4. Use it in a technical paper: If you are writing a technical paper, you can use the word homeomorphism to describe a mathematical concept.
For example, "The homeomorphism between the two spaces is a crucial aspect of the proof."
5. Use it in a sentence with other mathematical terms: You can use the word homeomorphism in a sentence with other mathematical terms to show your understanding of the subject.
For example, "The homeomorphism between the two spaces is continuous and bijective."
6. Use it in a sentence with a real-world application: You can use the word homeomorphism in a sentence with a real-world application to show its relevance.
For example, "The concept of homeomorphism is used in computer graphics to transform one image into another."
7. Use it in a sentence with a comparison: You can use the word homeomorphism in a sentence with a comparison to show the similarities or differences between two objects.
For example, "The homeomorphism between the two spaces is similar to the isomorphism between two groups."
In conclusion, using the word homeomorphism in a sentence requires an understanding of its meaning and context. By following these tips, you can use the word effectively in your writing and demonstrate your knowledge of mathematics.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Homeomorphism. They do not represent the opinions of TranslateEN.com.