Home U+2A00 to U+2AFF Supplemental Mathematical Operators

# U+2A33 SMASH PRODUCT

U+2A33 was added to Unicode in version 3.2 (2002). It belongs to the block U+2A00 to U+2AFF Supplemental Mathematical Operators in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. In text U+2A33 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

In topology, a branch of mathematics, the smash product of two pointed spaces (i.e. topological spaces with distinguished basepoints) (X, x0) and (Y, y0) is the quotient of the product space X × Y under the identifications (xy0) ∼ (x0y) for all x in X and y in Y. The smash product is itself a pointed space, with basepoint being the equivalence class of (x0, y0). The smash product is usually denoted X ∧ Y or X ⨳ Y. The smash product depends on the choice of basepoints (unless both X and Y are homogeneous).

One can think of X and Y as sitting inside X × Y as the subspaces X × {y0} and {x0} × Y. These subspaces intersect at a single point: (x0, y0), the basepoint of X × Y. So the union of these subspaces can be identified with the wedge sum X ∨ Y. The smash product is then the quotient

X ∧ Y = ( X × Y ) / ( X ∨ Y ) . {displaystyle Xwedge Y=(X imes Y)/(Xvee Y).}

The smash product shows up in homotopy theory, a branch of algebraic topology. In homotopy theory, one often works with a different category of spaces than the category of all topological spaces. In some of these categories the definition of the smash product must be modified slightly. For example, the smash product of two CW complexes is a CW complex if one uses the product of CW complexes in the definition rather than the product topology. Similar modifications are necessary in other categories.

## Representations

System Representation
10803
UTF-8 E2 A8 B3
UTF-16 2A 33
UTF-32 00 00 2A 33
URL-Quoted %E2%A8%B3
HTML-Escape &#x2A33;
Wrong windows-1252 Mojibake â¨³
HTML-Escape &smashp;

## Complete Record

Property Value
Age 3.2 (2002)
Unicode Name SMASH PRODUCT
Unicode 1 Name
Block Supplemental Arrows-C
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Smash Product
Lowercase
Simple Lowercase Mapping Smash Product
Lowercase Mapping Smash Product
Uppercase
Simple Uppercase Mapping Smash Product
Uppercase Mapping Smash Product
Simple Titlecase Mapping Smash Product
Titlecase Mapping Smash Product
Case Folding Smash Product
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Bidi Paired Bracket Smash Product
Bidi Paired Bracket Type None
Cased
Composition Exclusion
Case Ignorable
Full Composition Exclusion
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Dash
Deprecated
Default Ignorable Code Point
Diacritic
East Asian Width Neutral
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji
Emoji Presentation
Extender
Extended Pictographic
FC NFKC Closure Smash Product
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hangul Syllable Type Not Applicable
Hyphen
ID Continue
Ideographic
ID Start
IDS Binary Operator
IDS Trinary Operator and
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
ISO 10646 Comment
Joining Group No_Joining_Group
Join Control
Jamo Short Name
Joining Type Non Joining
Line Break Alphabetic
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Smash Product
NFKC Quick Check Yes
NFKD Quick Check Yes
Numeric Type None
Numeric Value not a number
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Pattern Syntax
Pattern White Space
Prepended Concatenation Mark
Quotation Mark
Regional Indicator
Sentence Break Other
Simple Case Folding Smash Product
Script Extension
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Vertical Orientation R
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD