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A rose with four petals. In mathematics, a rose (also known as a bouquet of n circles) is a topological space obtained by gluing together a collection of circles along a single point. The circles of the rose are called petals. Roses are important in algebraic topology, where they are closely related to free groups.
Rosa banksiae Rosa persica. There are currently four subgenera in Rosa, although there have been some disputes over the years. [3] The four subgenera are: Hulthemia (formerly Simplicifoliae, meaning "with single leaves") containing one or two species from Southwest Asia, R. persica and R. berberifolia (syn. R. persica var. berberifolia) which are the only species without compound leaves or ...
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
The rose family is considered one of the six most economically important crop plant families, [37] and includes apples, pears, quinces, medlars, loquats, almonds, peaches, apricots, plums, cherries, strawberries, blackberries, raspberries, sloes, and roses. Many genera are also highly valued ornamental plants.
The rosids are members of a large clade (monophyletic group) of flowering plants, containing about 70,000 species, [2] more than a quarter of all angiosperms. [3] The clade is divided into 16 to 20 orders, depending upon circumscription and classification. These orders, in turn, together comprise about 140 families. [4]
Rosales (/ r oʊ ˈ z eɪ l iː z /, roh-ZAY-leez) [5] are an order of flowering plants. [6] Well-known members of Rosales include: roses, strawberries, blackberries and raspberries, apples and pears, plums, peaches and apricots, almonds, rowan and hawthorn, jujube, elms, banyans, figs, mulberries, breadfruit, nettles, hops, and cannabis.
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; Cantor space; Co-kappa topology Cocountable topology; Cofinite topology; Compact-open topology; Compactification; Discrete topology; Double-pointed cofinite topology; Extended real number line; Finite topological space; Hawaiian earring; Hilbert cube
Absolutely closed See H-closed Accessible See . Accumulation point See limit point. Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of a poset.
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