Can Complex Spaces Be Projected onto Closed Real Spaces without Infinity?

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In summary, the conversation discusses the speaker's search for good reading material and references on a specific scenario involving projecting a 1 dimensional complex space onto a 1 dimensional closed real space in a way that avoids infinity values. They also express interest in extending this mapping to higher dimensions and inquire about any interesting results that may arise. They are looking for references from people who have studied this particular scenario.
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thehangedman
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I am looking for good reading material and references on something. I have tried the google route and can't find anything so I thought I would ask the community of people who know...

I want to learn more about the following scenario: Suppose I start with a 1 dimensional complex space. I want to project that onto a 1 dimensional closed (compacted?) real space. Essentially, map the complex plane to the real circle. I am also interested in this mapping in higher dimensions too, so C2 mapping to the real surface of a sphere. Caveat here, though, is that the real spaces should not have projected values of infinity. I would rather the coordinates loop (spherical would work better I'd assume). I was thinking along the line of projecting the complex plane to the unit circle in the plane and using the distance around said circle to create the compacted real space, but would that work in higher dimensions and does that yield any interesting results?

Again I'm not looking for any specific "answer" but rather references of people who have studied this specific scenerio and what they came up with.

Thanks for all your help!
 
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anyone?
 

FAQ: Can Complex Spaces Be Projected onto Closed Real Spaces without Infinity?

1. What is projection in science?

Projection in science refers to the process of representing a three-dimensional object or space onto a two-dimensional surface. It is commonly used in fields such as geography, cartography, and psychology to create maps, diagrams, and visualizations.

2. How is projection used in research?

Projection is used in research to accurately represent and analyze data and phenomena that exist in three-dimensional space. It allows researchers to visualize and communicate complex information in a simplified manner, making it easier to understand and draw conclusions.

3. What are the different types of projection?

There are several types of projection used in science, including cylindrical, conic, and azimuthal. Each type has its own unique properties and is best suited for specific purposes. For example, cylindrical projections are often used for mapping large areas, while azimuthal projections are useful for representing polar regions.

4. What are the advantages and disadvantages of projection?

The main advantage of projection is its ability to transform complex three-dimensional information into a simpler, two-dimensional representation. However, this simplification can also be a disadvantage, as it may distort or omit important details. Additionally, different projection methods can result in different interpretations of the same data.

5. How do scientists choose the appropriate projection for their research?

Choosing the appropriate projection for a specific research project depends on several factors, such as the purpose of the visualization, the type and scale of the data being represented, and the intended audience. Scientists often consider the strengths and limitations of different projection methods and select the one that best suits their research needs.

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