How Do You Spell CLOSE SET?

Pronunciation: [klˈə͡ʊs sˈɛt] (IPA)

The spelling of "close set" can be explained using the IPA phonetic transcription. The first word, "close", is pronounced as /kloʊs/, with the long "o" sound and the "s" sound at the end. The second word, "set", is pronounced as /sɛt/, with the short "e" sound and the "t" sound at the end. "Close set" typically refers to something that is placed tightly together or is physically near each other. The accurate spelling of the word is important for clear communication and understanding.

Meaning and Definition
Common Misspellings
Etymology
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CLOSE SET Meaning and Definition

  1. A close set refers to a subset within a larger mathematical set in which its complement, or elements not belonging to the set, are situated relatively far away. In other words, it is a collection of elements that are located close to each other while being distant from elements outside of the set.

    In the realm of topology, a close set is defined as a set that contains all of its limit points. A limit point is one that can be approached infinitely closely by other points within the set. Consequently, a close set consists of its limit points as well as all the points in the set itself. This implies that no limit point of a close set is found outside the set, a crucial characteristic distinguishing it from an open set.

    The concept of a close set plays a fundamental role in various areas of mathematics, such as analysis, topology, and geometry. It helps in studying the convergence, continuity, and connectedness of functions and spaces. For instance, in analysis, the closure of a set is obtained by considering the set along with all of its limit points, resulting in a close set.

    In summary, a close set is a subset of a larger set that includes all its limit points. It signifies the proximity and cohesion of elements within the set while being distant from elements outside of it.

Common Misspellings for CLOSE SET

Etymology of CLOSE SET

The term "close set" is composed of two parts: "close" and "set".

The word "close" comes from the Old French word "cloz", which means "closed" or "shut". This was derived from the Latin word "clausus", meaning "closed" or "shut". Over time, "close" evolved to have various meanings, including "near" or "tight".

The word "set" has Middle English roots and is derived from the Old English word "settan", meaning "to put" or "to place". It can also be traced back to the Old Norse word "setja".

When combined, "close set" refers to something that is situated or positioned near or tightly together, as well as having a compact arrangement.

Similar spelling words for CLOSE SET