# On the generation of a simple surface by means of a set of equicontinuous curves

Fundamenta Mathematicae (1923)

• Volume: 4, Issue: 1, page 106-117
• ISSN: 0016-2736

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## Abstract

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The purpose of this article is to prove: Theorem: Suppose that, in a given three dimensional space S, ABCD is a rectangle and G is a self-compact set of simple continuous arcs such that: 1. through each point of ABCD there is just one arc of G, 2. BC and AD are arcs of G, 3. no two arcs of G have a point in common, 4. each arc of G has one endpoint on the interval AB and one endpoint on the interval CD but contains no other point in common with either of these intervals, 5. the set of arcs G is equicontinous. Then the point - set R composed of all the arcs of the set G is in one to one continuous correspondence with the plane point-set formed by a rectangle together with its interior.

## How to cite

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Moore, Robert. "On the generation of a simple surface by means of a set of equicontinuous curves." Fundamenta Mathematicae 4.1 (1923): 106-117. <http://eudml.org/doc/213627>.

@article{Moore1923,
abstract = {The purpose of this article is to prove: Theorem: Suppose that, in a given three dimensional space S, ABCD is a rectangle and G is a self-compact set of simple continuous arcs such that: 1. through each point of ABCD there is just one arc of G, 2. BC and AD are arcs of G, 3. no two arcs of G have a point in common, 4. each arc of G has one endpoint on the interval AB and one endpoint on the interval CD but contains no other point in common with either of these intervals, 5. the set of arcs G is equicontinous. Then the point - set R composed of all the arcs of the set G is in one to one continuous correspondence with the plane point-set formed by a rectangle together with its interior.},
author = {Moore, Robert},
journal = {Fundamenta Mathematicae},
keywords = {krzywe jednakowociągłe; krzywa; krzywa prosta; powierzchnia},
language = {eng},
number = {1},
pages = {106-117},
title = {On the generation of a simple surface by means of a set of equicontinuous curves},
url = {http://eudml.org/doc/213627},
volume = {4},
year = {1923},
}

TY - JOUR
AU - Moore, Robert
TI - On the generation of a simple surface by means of a set of equicontinuous curves
JO - Fundamenta Mathematicae
PY - 1923
VL - 4
IS - 1
SP - 106
EP - 117
AB - The purpose of this article is to prove: Theorem: Suppose that, in a given three dimensional space S, ABCD is a rectangle and G is a self-compact set of simple continuous arcs such that: 1. through each point of ABCD there is just one arc of G, 2. BC and AD are arcs of G, 3. no two arcs of G have a point in common, 4. each arc of G has one endpoint on the interval AB and one endpoint on the interval CD but contains no other point in common with either of these intervals, 5. the set of arcs G is equicontinous. Then the point - set R composed of all the arcs of the set G is in one to one continuous correspondence with the plane point-set formed by a rectangle together with its interior.
LA - eng
KW - krzywe jednakowociągłe; krzywa; krzywa prosta; powierzchnia
UR - http://eudml.org/doc/213627
ER -

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