# 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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topMoore, 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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