analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
continuous metric space valued function on compact metric space is uniformly continuous
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A field with a notion of a limit of a function that satisfy the algebraic limit theorems.
Let $F$ be a Heyting field and a Hausdorff function limit space, where $x^{-1}$ is another notation for the reciprocal function $\frac{1}{x}$. $F$ is a algebraic limit field if the algebraic limit theorems are satisfied, i.e. if the limit preserves the field operations:
for all elements $c \in S$,
for all elements $c \in S$ and functions $f:S \to C$ and $g:S \to C$ such that
for all elements $c \in S$ and functions $f:S \to C$ such that
for all elements $c \in S$ and functions $f:S \to C$ and $g:S \to C$ such that
for all elements $c \in S$, integers $a \in \mathbb{Z}$, and functions $f:S \to C$, such that
for all elements $c \in S$ and $a \in S$, and functions $f:S \to C$, such that
for all elements $c \in S$,
for all elements $c \in S$ and functions $f:S \to C$ and $g:S \to C$ such that
for all elements $c \in S$, natural numbers $n \in \mathbb{N}$, and functions $f:S \to C$, such that
for all elements $c \in S$, and functions $f:S \to C$, such that
if
then
for all elements $c \in S$, and functions $f:S \to C$, such that
if
then
Last revised on May 4, 2022 at 19:41:09. See the history of this page for a list of all contributions to it.