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⨳

smash product

Smash Product

⨳ denotes the smash product, an operation on spaces with chosen points. In algebraic topology, the same operation is commonly written X ∧ Y; ⨳ is not ordinary multiplication.

Text symbol
Search it as
smash product formula · LaTeX \smashtimes · pointed spaces · topology operator
Shows up in
Anything that takes text · its shape is whatever your font draws

What ⨳ means

It combines pointed spaces and collapses their basepoint parts to one point.

A pointed space is a space with one chosen point, called its basepoint. For two such spaces, form every pair in their product, then identify all pairs whose first or second coordinate is a basepoint as one shared point. The resulting space is their smash product.

Why is ∧ smash product notation?

It is a common notation for this operation in algebraic topology.

Formulas often write the smash product as X ∧ Y. The same ∧ sign means logical AND elsewhere, so the surrounding formula matters; ⨳ names the smash product directly.

Don't confuse it with

4

Questions people ask

1

Why does ⨳ show as a box on some devices?

Because that device's fonts have no glyph for it. The character is still correct and still copies correctly — the box is a missing glyph, not a broken character.

How to type ⨳

Windows (Word)
Alt+XType 2A33, then Alt+X to get ⨳.
Windows
Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win + .).
macOS
Control+Command+SpaceOpen the character viewer and search “smash product”.
Linux
Ctrl+Shift+UType 2a33, then Enter or Space.
HTML
⨳
CSS
\2A33
LaTeX: \smashtimes
With LaTeX's unicode-math package, \smashtimes produces ⨳ as of 2026-10-08.
Codes and encoding1 code points
HTML decimal
⨳
HTML hex
⨳
CSS content
content: "\2A33";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%A8%B3
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

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Maths & numbers1,835 symbols