Verb

(involv)

To roll or fold up; to wind round; to entwine.

* (John Milton)

Some of serpent kind involved / Their snaky folds.

To envelop completely; to surround; to cover; to hide; to involve in darkness or obscurity.

* (John Milton)

And leave a singèd bottom all involved / With stench and smoke.

To complicate or make intricate, as in grammatical structure.

* (John Locke)

Involved discourses.

*{{quote-book, year=1963, author=(Margery Allingham), title=(The China Governess)

, chapter=17 citation , passage=The face which emerged was not reassuring. […]. He was not a mongol but there was a deficiency of a sort there, and it was not made more pretty by a latter-day hair cut which involved eccentrically long elf-locks and oiled black curls.}}

To connect with something as a natural or logical consequence or effect; to include necessarily; to imply.

* (John Milton)

He knows / His end with mine involved .

* Tillotson

The contrary necessarily involves a contradiction.

*{{quote-magazine, year=2013, month=July-August, author= Sarah Glaz

, title= Ode to Prime Numbers , volume=101, issue=4, magazine=(American Scientist) , passage=Some poems, echoing the purpose of early poetic treatises on scientific principles, attempt to elucidate the mathematical concepts that underlie prime numbers. Others play with primes’ cultural associations. Still others derive their structure from mathematical patterns involving primes.}}

To take in; to gather in; to mingle confusedly; to blend or merge.

* (Alexander Pope)

The gathering number, as it moves along, / Involves a vast involuntary throng.

* (John Milton)

Earth with hell / To mingle and involve .

To envelop, enfold, entangle, or embarrass.

To engage thoroughly; to occupy, employ, or absorb.

* Sir (Walter Scott)

Involved in a deep study.

(mathematics) To raise to any assigned power; to multiply, as a quantity, into itself a given number of times.

Verb

(immers)

To put under the surface of a liquid; to dunk.

Archimedes determined the volume of objects by immersing them in water.

To involve deeply

The sculptor immersed himself in anatomic studies.

(mathematics)

* 2002 , Kari Jormakka, Flying Dutchmen: Motion in Architecture (page 40)

Thus, in mathematical terms a Klein bottle cannot be "embedded" but only "immersed " in three dimensions as an embedding has no self-intersections but an immersion may have them.