इंग्रजी मध्ये HOMEOMORPHIC म्हणजे काय?
होमोमोर्फिझम
टोपोलॉजीच्या गणिताच्या क्षेत्रात, होमोमोर्फिझम किंवा टोपोलॉजिकल आइसोमोर्फिफम किंवा दोन निरंतर फलन अवकाशासंबंधी अंतर असणारे सतत अवयवांचे कार्य आहे ज्यामध्ये सतत व्यस्त वर्तन असते. होमोमोर्फिज्म हा टोपोलॉजिकल स्पेसच्या श्रेणीमधील समस्थानिक आहे-म्हणजे ते मॅपिंग आहेत जे दिलेल्या स्पेसच्या सर्व विषम गुणधर्मांचे रक्षण करते. त्यांच्यात होमोमोर्फिझमसह दोन जागा होमोमोर्फिक म्हटल्या जातात आणि एक टॉपोलिक दृष्टिकोनातून ते समान आहेत. शब्द homomorphism ग्रीक शब्द ὅμοιος = समान आणि μορφή = आकार, फॉर्म पासून येतो. जवळजवळ एक अवकाशात्मक स्थान एक भूमितीय वस्तु आहे, आणि होमोमोर्फिझम एक नवीन आकारात सतत ओढणे आणि झटकन आहे. अशाप्रकारे, एक चौरस आणि एक वर्तुळ एकमेकांना होमऑमॉर्फिक असतात, पण एक गोल आणि एक तोड नाही. एक अनेकवेळा पुनरावृत्ती झालेले गणिती विनोद म्हणजे त्यांच्यात त्यांच्या कॉफीच्या कपमधून आपल्या कॉफीच्या कपला सांगता येत नाही, कारण डू डूटाचे रूपांतर एका कॉफी कपच्या स्वरूपात केले जाऊ शकते. कपचे हँडल
इंग्रजी शब्दकोशातील homeomorphic व्याख्या
शब्दकोशमध्ये होमोमोर्फिकची परिभाषा समान क्रिस्टल स्वरूपाची आहे परंतु भिन्न रासायनिक रचना आहे. होमोमोर्फिकची दुसरी परिभाषा एक-टू-एक पत्रव्यवहार असलेली आहे, दोन्ही दिशांनी निरंतर.
«HOMEOMORPHIC» संबंधित इंग्रजी पुस्तके
खालील ग्रंथसूची निवडीमध्ये
homeomorphic चा वापर शोधा. इंग्रजी साहित्यामध्ये वापराचा संदर्भ देण्यासाठी
homeomorphic शी संबंधित पुस्तके आणि त्याचे थोडक्यात उतारे.
(f ) In R, any two intervals that look alike are homeomorphic. [ 0, 1 ] and [ a, b ] are
homeomorphic, as are (0, 1) and (a. b). The interval (0, 1) is also homeomorphic
to R, and (0, 1 ] is homeomorphic to [a, b). Why? [Hint: The map x H> 2 - 3x is a ...
Thus, the relation “is homeomorphic to" is an equivalence relation on any set of
topological spaces. The reader might profit from thinking, at this point, about the
question: is there a set of all topological spaces? To prove two spaces are ...
For example, if we take the region of S2 to the south of the equator (or any fixed
latitude), then this is homeomorphic to a disc (closed or open according to
whether or not we include the equator) under stereographic projection. So, for
example ...
(b) Any two closed intervals are homeomorphic, and any two half- open intervals
are homeomorphic. (c) No open interval is homeomorphic to a closed or half-
open interval, and no closed interval is homeomorphic to a half-open interval.
5
Mathematical Analysis: Linear and Metric Structures and ...
6.72 ![. Show that the unit circle S1 of R2 is not homeomorphic to R. [Hint:
Suppose h : S1 — > R is a homeomorphism and let io £ S1. Then S1 \ {xo} is
connected, while R \ {h(xo)} is not connected.] 6.73 Theorem. In R each closed
interval is ...
Mariano Giaquinta, Giuseppe Modica,
2007
6
A Basic Course in Algebraic Topology
Such an open tube or cylinder is homeomorphic to a sphere with two holes cut in
it, and forming the connected sum of S with a sphere does not change anything.
Thus, the space resulting from the first stage is homeomorphic to the original ...
The closed interval / = [0, 1] and the open interval / = (0,1) are not homeomorphic.
Assume the converse and let /:/-»/ be a homeomorphism. The point 1 does not
divide the closed interval / , i.e., after it is removed any two remaining points can ...
Viktor Vasilʹevich Prasolov,
1995
than 1, to the whole of Rn. In particular the open interval ] − 1,1[ is homeomorphic
to the whole real line. In the next two examples we make use of the transitivity
property of being homeomorphic: if S is homeomorphic to T,andT is ...
Stephen Huggett, David Jordan,
2009
We intuitively feel, however, that if n # m, then R" is not homeomorphic to R“. In
order to confirm our intuitive feeling, we would have to find some topological
property of R" which is not possessed by R“. In its full generality, this problem is
not ...
Michael C. Gemignani,
1972
X and Y are homeomorphic. written X ~ Y, if there exists a homeomorphism /: X —
> Y. Example 3 An open interval (a. b) is homeomorphic to the real line, (a. b) ~ R
. For example, the map /:(0,l)-> is a homeomorphism. illustrated in Figure 7.3a.
Miles Reid, Balazs Szendroi,
2005
नवीन गोष्टी ज्यामध्ये «HOMEOMORPHIC» ही संज्ञा समाविष्ट आहे
खालील बातम्यातील आयटमच्या संदर्भात राष्ट्रीय आणि आंतरराष्ट्रीय पत्रकार कशाबद्दल बोलले आहेत आणि
homeomorphic ही संज्ञा कशी वापरली आहे ते शोधा.
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