COMPACTIFIES Meaning and
Definition
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The term "compactifies" is a verb that refers to the process of transforming or modifying a mathematical space in order to obtain a compact space. In mathematics, a compact space is one that is closed and bounded, ensuring that every sequence or subset in the space has a limit or adheres to certain properties.
When applied to a specific mathematical space, such as a topological, differential, or algebraic space, the process of compactification involves introducing additional points or boundaries to the original space. These additional points serve to capture the behavior of sequences or subsets that diverge or go off to infinity in the original space.
By compactifying a space, mathematicians are able to study the entirety of its points, including those at infinity or in the boundary regions, and analyze the behavior of its elements in a more comprehensive manner. Compactification is a crucial tool in many branches of mathematics, such as topology, where it allows for the exploration of the properties of infinite structures.
In summary, the verb "compactifies" refers to the act of modifying a mathematical space by introducing additional points or boundaries in order to obtain a compact space, thereby enabling a more thorough analysis of the elements within the space.
Etymology of COMPACTIFIES
The word "compactify" is derived from the combination of two words: "compact" and "-ify".
The term "compact" comes from the Latin word "compactus", which means "close, firm, or solid". In mathematics, a "compact" object refers to a space or set that is closed, bounded, and has no infinite sequences that diverge to infinity.
The suffix "-ify" originates from the Latin suffix "-ficare", which means "to make" or "to cause". It is commonly used in English to form verbs from nouns or adjectives, indicating the process of causing or making something.
Therefore, "compactify" is formed by combining "compact" with the suffix "-ify", resulting in a verb that refers to the process of making or causing something to be compact.
Conjugate verb Compactifies
CONDITIONAL
I
would compactifies
you
would compactifies
he/she/it
would compactifies
we
would compactifies
they
would compactifies
CONDITIONAL CONTINUOUS
I
would be compactifiesing
you
would be compactifiesing
he/she/it
would be compactifiesing
we
would be compactifiesing
they
would be compactifiesing
CONDITIONAL PERFECT
I
would have compactifies
you
would have compactifies
he/she/it
would have compactifies
we
would have compactifies
they
would have compactifies
CONDITIONAL PERFECT CONTINUOUS
I
would have been compactifiesing
you
would have been compactifiesing
he/she/it
would have been compactifiesing
we
would have been compactifiesing
they
would have been compactifiesing
FUTURE
I
will compactifies
you
will compactifies
he/she/it
will compactifies
we
will compactifies
they
will compactifies
FUTURE CONTINUOUS
I
will be compactifiesing
you
will be compactifiesing
he/she/it
will be compactifiesing
we
will be compactifiesing
they
will be compactifiesing
FUTURE PERFECT
I
will have compactifiesed
you
will have compactifiesed
he/she/it
will have compactifiesed
we
will have compactifiesed
they
will have compactifiesed
FUTURE PERFECT CONTINUOUS
I
will have been compactifiesing
you
will have been compactifiesing
he/she/it
will have been compactifiesing
we
will have been compactifiesing
they
will have been compactifiesing
IMPERATIVE
you
compactifies
we
let´s compactifies
to compactifies
PAST
I
compactifiesed
you
compactifiesed
he/she/it
compactifiesed
we
compactifiesed
they
compactifiesed
PAST CONTINUOUS
I
was compactifiesing
you
were compactifiesing
he/she/it
was compactifiesing
we
were compactifiesing
they
were compactifiesing
PAST PARTICIPLE
compactifiesed
PAST PERFECT
I
had compactifiesed
you
had compactifiesed
he/she/it
had compactifiesed
we
had compactifiesed
they
had compactifiesed
PAST PERFECT CONTINUOUS
I
had been compactifiesing
you
had been compactifiesing
he/she/it
had been compactifiesing
we
had been compactifiesing
they
had been compactifiesing
PRESENT
I
compactifies
you
compactifies
he/she/it
compactifieses
we
compactifies
they
compactifies
PRESENT CONTINUOUS
I
am compactifiesing
you
are compactifiesing
he/she/it
is compactifiesing
we
are compactifiesing
they
are compactifiesing
PRESENT PARTICIPLE
compactifiesing
PRESENT PERFECT
I
have compactifiesed
you
have compactifiesed
he/she/it
has compactifiesed
we
have compactifiesed
they
have compactifiesed
PRESENT PERFECT CONTINUOUS
I
have been compactifiesing
you
have been compactifiesing
he/she/it
has been compactifiesing
we
have been compactifiesing
they
have been compactifiesing
