Math@Funny@Honey@Money

أسرة الموقع ترحب بك و نتمنى أن تكون بتمام الصحة و العافيه
Math@Funny@Honey@Money



    mathematical def. and some theorems

    شاطر
    avatar
    teacher
    ناظر
    ناظر

    ذكر
    عدد الرسائل : 439
    العمر : 30
    Location : Egypt
    Job/hobbies : learner
    Skills/Courses : egypt
    Mood :
    الأوسمة :
    تاريخ التسجيل : 05/04/2008

    mathematical def. and some theorems

    مُساهمة من طرف teacher في الجمعة 16 مايو 2008, 5:15 pm

    [edit] Mathematical definition



    Main article: Topological space
    Let X be any set and let T be a family of subsets of X. Then T is a topology on X if


    1. Both the empty set and X are elements of T.
    2. Any union of arbitrarily many elements of T is an element of T.
    3. Any intersection of finitely many elements of T is an element of T.
    If T is a topology on X, then X together with T is called a topological space.
    All sets in T are called open; note that in general not all subsets of X need be in T. A subset of X is said to be closed if its complement is in T (i.e., it is open). A subset of X may be open, closed, both, or neither.
    A function or map from one topological space to another is called continuous if the inverse image of any open set is open. If the function maps the real numbers to the real numbers (both space with the Standard Topology), then this definition of continuous is equivalent to the definition of continuous in calculus. If a continuous function is one-to-one and onto and if the inverse of the function is also continuous, then the function is called a homeomorphism and the domain of the function is said to be homeomorphic to the range. Another way of saying this is that the function has a natural extension to the topology. If two spaces are homeomorphic, they have identical topological properties, and are considered to be topologically the same. The cube and the sphere are homeomorphic, as are the coffee cup and the doughnut. But the circle is not homeomorphic to the doughnut.

    [edit] Some theorems in general topology


    General topology also has some surprising connections to other areas of mathematics. For example:


    santa


    _________________
    واخر دعوانا ان الحمد لله رب العالمين
    avatar
    Asmaa Mahmoud
    Site Administrator
    Site Administrator

    انثى
    عدد الرسائل : 982
    العمر : 30
    Location : egypt / Giza
    Job/hobbies : math teacher
    Skills/Courses : thinking
    Mood :
    الأوسمة :
    تاريخ التسجيل : 27/03/2008

    رد: mathematical def. and some theorems

    مُساهمة من طرف Asmaa Mahmoud في السبت 17 مايو 2008, 4:46 pm

    thank's alot shady
    u r very strong in your topics
    _________________


    _________________
    ][/url]




      الوقت/التاريخ الآن هو الإثنين 20 نوفمبر 2017, 9:49 am