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This is a textbook aimed at the level of advanced undergraduates or beginning graduate students in mathematics, [2] perhaps after having already completed a first course in topology. Readers of the book are expected to already be familiar with general topology , linear algebra , and group theory . [ 1 ]
The Board of Secondary Education, Karachi is a government board in Karachi for secondary education examination. It was established in 1950 by the promulgation of the Central Legislative Act No. XVI of 1950. [1] BSEK controls and organizes the secondary education examinations in Karachi.
The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. This is a list of topology topics. See also: Topology glossary; List of topologies; List of general topology topics; List of geometric topology topics
The Education and Literacy Department is a key division of the Government of Sindh, Pakistan, responsible for overseeing the provincial's education system.Its primary role is to manage educational affairs within Sindh and coordinate with the Federal Government and donor agencies to promote education.
Board Established City Website Refs Catholic Board of Education, Pakistan: 1961 Karachi [47] Lahore [48] [49] Diocesan board of education, Pakistan 1960 Islamabad, Rawalpindi [50] [51] Presbyterian Education Board Pakistan Lahore, Punjab
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.. Non-simply connected 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups. [1]
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a function whose domain is a directed set. The codomain of this function is usually some topological space. Nets directly generalize the concept of a sequence in a metric space.
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