Category:Metric Space Theorems

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Pages in category "Metric Space Theorems"

The following 36 pages are in this category, out of 36 total.

1

UTLOC:1

A

A function is continuous if and only if the pre-image of every basis element is open
A monotonically increasing sequence bounded above converges
A set is bounded if and only if for all points in the space there is a positive real such that the distance from that point to any point in the set is less than the positive real
A set is dense if and only if every non-empty open subset contains a point of it
A subset of a topological space is open if and only if it is a neighbourhood to all of its points
An open ball contains another open ball centred at each of its points
An open set is a neighbourhood to all of its points

C

D

Discrete metric and topology/Summary

E

G

Given two open balls sharing the same centre but with differing radius then the one defined to have a strictly smaller radius is contained in the other

I

L

Lebesgue number lemma

M

Metric topology

O

Operations on convergent sequences of real numbers

T

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