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# proximity continuous

Let $(P,\delta)$ and $(Q,\epsilon)$ be proximity spaces.

A function $f:P\to Q$ is said to be *proximity continuous* if for any subsets $A,B\subseteq P$, $A\mathrel{\delta}B$ implies that $f(A)\mathrel{\epsilon}f(B)$.

Defines:

$\delta$-continuous

Keywords:

proximity space, nearness space, proximity continuity

Synonym:

near-continuousness

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54C08*no label found*54C05

*no label found*54E17

*no label found*54E05

*no label found*

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## Corrections

clarify by CWoo ✓

grammar ("be", not "are") by Wkbj79 ✓

capitalization of title by Mathprof ✓

consider rephrasing by CWoo ✓

near by CWoo ✓

grammar ("be", not "are") by Wkbj79 ✓

capitalization of title by Mathprof ✓

consider rephrasing by CWoo ✓

near by CWoo ✓