Determining discrete topology

Reference no: EM13134653

A covering map is a map p: E -> B with the property that each point b, an element of B, has a neighborhood U such that p^-1(U) is a disjoint union of open sets V_alpha such that, for each alpha, the restriction of p to V_alpha is a homeomorphism of V_alpha onto U.

Show that, if Y has the discrete topology and if p: X x Y --> X is the projection onto the first factor, then p is a covering map.

Reference no: EM13134653

Questions Cloud

Volume of solid below paraboloid : Use polar coordinates to evaluate the volume of the solid below the paraboloid (z= 4-x^2-y^2) and above the xy plane.

What is the residual income : Ruger has a profit margin of 16% based on revenues of $400,000 and an investment turnover is 2. What is the residual income when the cost of capital is 10%?

What are the main distinctions that you would see : Financial reporting for a special-purpose local government depends upon whether that government is engaged in governmental-type activities, business-type activities only, or fiduciary-type activities only.

Probability that individual will be able to keep eye contact : The length of time recorded is normally distributed with a mean of 184 seconds and a standard deviation of 55 seconds. What is the probability that and individual will be able to keep eye contact longer than 239 seconds?

Determining discrete topology : A covering map is a map p: E -> B with the property that each point b, an element of B, has a neighborhood U such that p^-1(U) is a disjoint union of open sets V_alpha

Define interperiod income tax allocation : Define interperiod income tax allocation and briefly explain the three methods that have been advocated. Conclude by summarizing the generally accepted accounting principles for interperiod income tax allocation.

Concept of straight-line depreciation : Stevens Co. bought a machine on January 1, 2008 for $875,000. It had a $25,000 estimated residual value and a ten-year life. An expense account was debited on the purchase date. Stevens uses straight-line depreciation.

Dehydration same care for all? : Dehydration same care for all?

How many different tetrapeptides containing molecules : How many different tetrapeptides containing 2 molecules of alanine and 2 molecules of valine could theoretically exist?

User Account

All Pages