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A homotopy between two embeddings of the torus into : as "the surface of a doughnut" and as "the surface of a coffee mug".This is also an example of an isotopy.. Formally, a homotopy between two continuous functions f and g from a topological space X to a topological space Y is defined to be a continuous function: [,] from the product of the space X with the unit interval [0, 1] to Y such that ...
The words bow and bough are examples where there are two meanings associated with a single pronunciation and spelling (the weapon and the knot); two meanings with two different pronunciations (the knot and the act of bending at the waist), and two distinct meanings sharing the same sound but different spellings (bow, the act of bending at the ...
When the prefix "re-" is added to a monosyllabic word, the word gains currency both as a noun and as a verb. Most of the pairs listed below are closely related: for example, "absent" as a noun meaning "missing", and as a verb meaning "to make oneself missing". There are also many cases in which homographs are of an entirely separate origin, or ...
For example, the letters b and v are pronounced exactly alike, so the words basta (coarse) and vasta (vast) are pronounced identically. [7] Other homonyms are spelled the same, but mean different things in different genders. For example, the masculine noun el capital means 'capital' as in 'money', but the feminine noun la capital means 'capital ...
A homograph (from the Greek: ὁμός, homós 'same' and γράφω, gráphō 'write') is a word that shares the same written form as another word but has a different meaning. [1] However, some dictionaries insist that the words must also be pronounced differently, [ 2 ] while the Oxford English Dictionary says that the words should also be of ...
(often spelled "kabob" in the US) meat served on a skewer together with onions, tomatoes, etc. (e.g. shish kebab) keen very low or competitive (price) eager or intent on, example: he is keen to get to work on time. desirable or just right, example: "peachy keen" – "That's a pretty keen outfit you're wearing." (slang going out of common usage)
In the case of homotopy, the continuous deformation from one map to the other is of the essence, and it is also less restrictive, since none of the maps involved need to be one-to-one or onto. Homotopy does lead to a relation on spaces: homotopy equivalence. There is a name for the kind of deformation involved in visualizing a homeomorphism.
The same homotopy category can arise from many different model categories. An important example is the standard model structure on simplicial sets : the associated homotopy category is equivalent to the homotopy category of topological spaces, even though simplicial sets are combinatorially defined objects that lack any topology .