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The smash product of any pointed space X with a 0-sphere (a discrete space with two points) is homeomorphic to X. The smash product of two circles is a quotient of the torus homeomorphic to the 2-sphere. More generally, the smash product of two spheres S m and S n is homeomorphic to the sphere S m+n.
A further construction in A 1-homotopy theory is the category SH(S), which is obtained from the above unstable category by forcing the smash product with G m to become invertible. This process can be carried out either using model-categorical constructions using so-called G m -spectra or alternatively using infinity-categories.
The smash product of spectra extends the smash product of CW complexes. It makes the stable homotopy category into a monoidal category; in other words it behaves like the (derived) tensor product of abelian groups. A major problem with the smash product is that obvious ways of defining it make it associative and commutative only up to homotopy.
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid-shaped region where a particular celestial body exerts the main gravitational influence on an orbiting object. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as moons , despite the ...
The radius of the sphere of influence is called the "(gravitational) influence radius". There are two definitions in common use for the radius of the sphere of influence. The first [ 1 ] is given by r h = G M BH σ 2 {\displaystyle r_{h}={\frac {GM_{\text{BH}}}{\sigma ^{2}}}} where M BH is the mass of the black hole, σ is the stellar velocity ...
By Giuseppe Fonte and Angelo Amante. ROME (Reuters) - When Italian Prime Minister Giorgia Meloni took office in 2022 she inherited a double whammy - the country not only had a worryingly low ...
In algebraic topology, Hilton's theorem, proved by Peter Hilton , states that the loop space of a wedge of spheres is homotopy-equivalent to a product of loop spaces of spheres. John Milnor ( 1972 ) showed more generally that the loop space of the suspension of a wedge of spaces can be written as an infinite product of loop spaces of ...
Michael J. Fox appears to be heading back to the future — at least when it comes to putting his memories of the popular film trilogy on paper.. After taking home the George Pal Memorial Award at ...